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SIMMs hEVELLFNC. 



U.Van Wostraaid/Publislier, NX 



A TREATISE 



PRINCIPLES AND PEACTICE 

OP 

LEVELLING, 

SHOWING ITS APPLICATION TO PUEPOSES OP 

RAILWAY ENGINEERING AND THE CONSTRUCTION OF ROADS, &o. 

/ » 

FREDERICK W. SIMMS, F. G. S., M. Inst. 0. E., 

CIVIL ENGINEEB. 

FIFTH EDITION, REVISED AND CORRECTED. 

WITH THE ADDITION OP 

MR. LAW'S 
i 

PRACTICAL EXAMPLES FOR SETTING OUT RAILWAY CURVES. 






'% 



Wify i\m £%gra$ |latw anb seforal WLoob-€vA*. 



NEW YORK: 
D. VAN NOSTRAND, PUBLISHER, 

23 Mueeay Street and 27 Waeeen Steeet. 

1870. 



-Ssf 




CONTENTS. 



PART I. 
ON THE PEINOIPLES OF LEVELLING. 

PAGE 

FlGURE OP THE EAETH 5 

Difference between the True and Apparent Level 9 

kule for computing ditto 10 

Example of computing ditto 10 

Table of the Difference of the Apparent and True Level for Dis- 
tances in Miles 12 

Table of ditto for Distances in Chains 13 

Logarithmic Kule for computing ditto 14 

Levelling Instruments 16 

The Y Level, 

Troughton's Improved Level, 

Dumpy Level. 

Levelling Staves, 

The Iron Tripod, 

The Measuring Chain. 

On Instrumental Parallax 23 

On the Principles of the Telescope, and of the Line of Collimation . 25 

Arrangement of Levelling Operations. 28 

PART II. 

THE PRACTICE OF LEVELLING. 

On Running or Check Levels 33 

Adjusting the Instrument for Observation, Etc 35 

Example of Field-Work 44 

Levels for the Formation of a Section 46 

Example of Field-Book 50 

Explanation of Field-Book 51 

Reduction of Levels 52 

To Draw the Section 57 

Working Section 61 

To Draw the Section 66 

Standard Levels 73 

Levelling with the Theodolite 73 



CONTENTS. 



PART III. 

COMPUTATION OF EARTH-WOKE, ROAD-MAKING, THE 
CLINOMETER, ETC. 

PAGE 

Application 01? a Section to Peactical Purposes 79 

To draw Lines of Intended Surface on Sections, to Arrange judi- 
ciously the Earth-Work . v 80 

Prismoidal Formula 84 

Example of Computation of Earth- Work 84 

Sir John Macneill's Tables — Cuttings and Embankments 91 

Slopes, Etc '. 95 

Description of the Clinometer 96 

Table of Slopes corresponding to given Angles 98 

On selecting a Line of Country for a Road or Railway 100 

Mr. Telford's Rules for Making and Repairing Roads 104 

Shape or Transverse Section 105 

Drainage 105 

Fences 106 

Road Materials 106 

The Foundation and Disposition of Materials 108 

Repairing Roads 109 

Level employed in the Construction of Roads Ill 

TABLES. 

I. Reduction from Hypothenusal to Horizontal Measure. 113 

II. Gradients or Inclined Planes 114 

Appendix 115 

Setting out Railways, Canals, Etc 117 

Modes oi Setting out Railway Curves, by Mr. Law 135 



A TREATISE ON LEVELLING. 



PART I. 



ON THE PRINCIPLES OF LEVELLING. 

Levelling is the art of tracing a line at the surface 
of the earth which shall cut the directions of gravity 
everywhere at right angles. If the earth were an ex- 
tended plane, all lines representing the direction of 
gravity at every point on its surface would be parallel 
to each other ; but, in consequence of its figure being 
that of a sphere or globe,* they everywhere converge 
to a point within the sphere which is equidistant from 
all parts of its surface ; or, in other words, the direction 
of gravity invariably tends towards the centre of the 
earth, and may be considered as represented by a 



* The figure of the earth is not exactly that of a sphere, but of an oblate 
spheroid flattened at the poles ; the length of the equatorial diameter being 
7924 miles, and that of the polar diameter 7898 miles. For our present pur- 
pose, it is sufficiently correct to consider it as a sphere. 



A TREATISE 



plumb-line when hanging freely, and suspended beyond 
the sphere of attraction of the surrounding objects. 



' 


» S ? 




< 


' J 


; 


; 




__-^-^_zx___ 






A 




I 






B 




c 




D 






E 





In the above diagram let the straight line A B repre- 
sent the surface of the earth, upon the supposition of 
its being an extended plane, the direction of gravit}^ at 
the points A, I, and B, would be represented by the 
lines AC, ID, and B E, all parallel to each other, and 
at right angles to the horizontal line A B. Now if the 
surface was modulatory, as shown by the curved line 
A B, and it was required to make a section represent- 
ing it, an instrument capable of tracing out a line 
parallel to the horizontal line A B (as a spirit level), 
might be set up anywhere on the surface, as at I, and 
staves being placed or held along the line, as at a, b, c, 
d, &c, the different heights above the ground where 
such staves were intersected by the line so traced out, 
would at once show the relative level of all those points, 
with regard to the horizontal line, as a datum or stand- 
ard of comparison. 



ON LEVELLING. 



But as the earth is a globe, its circumference must 
be circular, as I K L in the annexed figure ; the straight 
line A B will therefore not represent the surface of the 



h n B 




earth, but the sensible horizon of an observer stationed 
at the point I, to which point it is a tangent, being at 
right angles to the radius of the circle (or semi- 
diameter of the earth), I C. A line which is parallel 
to the sensible horizon of the observer, is the line 
traced out by our spirit-levels ; it is parallel to a tan- 
gent to the earth's surface at that point only where the 
instrument is set up, — thus A B is a tangent at I, and 
D E a tangent at F ; such being the fact, the difference 
of level between any two points cannot be determined 
by simple reference to a horizontal line, since every 
point on the surface of the globe (however near to each 
other) has a distinct horizon of its own. 

If the earth were everywhere surrounded by a fluid 
at rest, or that its surface was smooth, regular, and 
uniform, every point thereon would be equally distant 



8 A TREATISE 

from the centre ; but in consequence of the undulating 
form of the surface, places and objects are differently 
situated, some further from, and others nearer to, the 
centre of the earth, and consequently at different levels. 
The operation of levelling may therefore be defined as 
the art of finding how much higher or lower any one 
point is than another, or, more properly, the difference 
of their distances from the centre of the earth. 

Referring to our last figure, we have seen that the 
line A B is a true horizontal or level line at the point 
I, but being produced in the direction A or B, rises 
above the earth's surface ; and although it may appear 
to be level as seen from I, yet it is above the true level 
(which is represented by the circumference of the cir- 
cle) at every other point, and continues to diverge from 
it the further it is produced ; at Gr, the apparent line 
of level, as the horizontal line A B is called, is above 
the true level, by the distance Gr H, and at M by the 
distance M N, the difference being equal to the excess of 
the secant of the arc of distance above the radius of the 
earth. 

The difference, G H, or M N (see last figure), be- 
tween the true and apparent level may be thus found : 
put t in the adjoining diagram for the tangent IH,r for 
the radius C I of the earth, and x for Gr H, the excess 
of the secant of the arc of distance above the radius. ; 
I H being considered as equal to I Gr ; then 



ON LEVELLING. V 

or r 2 -{-2rx-\-x 2 ==r-\-t 2 
and 2 rx-^x 2 =-t 2 
or (2r-\-x) x = t 2 

But because the diameter of the earth 2 r is so great 
with respect to the quantity (x) sought, at all distances 




to which a common levelling operation usually extends, 
that 2r-\-x without sensible error may be replaced by 
2r, we then have 

2rx = t 2 
and x = — . 

Or in words : The difference (x) between the true and 
apparent level is equal to the square of the distance (t 2 ) 
divided by the diameter of the earth (2 r), and con- 
sequently is always proportional to the square of the 
distance. 

The mean diameter of the earth is 7916 miles, and 

the excess of the apparent above the true level for one 
t 2 



mile 



2r 



h-a of a mile, or 8.004 inches. At two 



TT16 



10 A TREATISE 

miles, it is four times that quantity, or 32.016 inches ; 
at three miles, it is nine times that quantity, or 72.036 
inches ; and so on increasing in proportion to the 
square of the distance. If we reject the decimal .004, 
and assume the difference between the true and appa- 
rent level for one mile to be exactly eight inches, or 
two-thirds of a foot, there arises the following con- 
venient form for computing the correction of level due 
to the curvature of the earth, for distances given in 
miles, which may easily be remembered : 

2D 2 

correction = — «— ' 

D being the distance in miles. Or in words : Two- 
thirds of the square of the distance in miles will be the 
amount of the correction in feet. 

Example. 

From a point on the Folkstone road, the top of the 
keep of Dover Castle was observed to coincide with the 
horizontal wire of a levelling telescope when adjusted 
for observation, and therefore was apparently on the 
same level ; the distance (D) from the instrument to 
the Castle was four miles and a-half ; consequently, 

D 2 =20.25 

2D 2 =40.50 

2 D 2 
3 = 13.5 feet, the correction required. 

From this it appears, that the keep of Dover Castle 
was 13.5 feet higher than the centre of the telescope on 



ON LEVELLING. 11 

the Folkstone road ; but on account of the curvature 
of the earth, it was apparently depressed to the same 
level. 

But the effect of the earth's curvature is modified by 
another cause, arising from optical deception ; namely 
Refraction. An object is never seen by us in its true 
position, but in the direction of the ray of light which 
conveys the impression or image of the object to our 
senses. Now the particles of light, in traversing the 
atmosphere, are, by the force of superior attraction? 
refracted or bent continually towards the perpendicular, 
as they penetrate the lower or denser strata ; and con- 
sequently they describe a curved track, of which the 
last portion, or its tangent, indicates the apparent ele- 
vated situation of a remote point. This trajectory, 
suffering almost a regular inflexure, may be considered 
as very nearly an arc of a circle, which has for its radius 
seven times the radius of our globe ; in consequence of 
which, the distance at which an object can be seen by 
the aid of refraction, is to the distance at which it could 
be seen without that aid, nearly as 14 to 13, the refrac- 
tion augmenting the distance at which an object can 
be seen by about a thirteenth of itself. Hence, to cor- 
rect the error occasioned by refraction, it will only be 
requisite to diminish the effects of the earth's curvature, 
or height of the apparent above the true level, by one- 
seventh of itself. Thus for our example of Dover 
Castle, \ of 13.5, or J -f-* i - = 1.93 feet nearly, to be sub- 
stracted from 13.5, which leaves 11.57 feet for the 



12 



A TREATISE 



height of Dover Castle above the level of a certain 
point on the Folkstone road. 

The following Tables show the reduction of the ap- 
parent to the true level, both for the curvature of the 
earth only, and also for the combined effects of curva- 
ture and refraction. The first gives the corrections 
corresponding to distances expressed in miles, and the 
second for distances in chains. 



Table of the Difference of the Apparent and True Level for 
Distances in Miles. 





CORRECTION. 


Distance 






in 

Miles. 


Curvature. 


Curvature and Refraction. 




feet. inches. 


feet. inches. 


i 


0.5 


0.4 


i 


2.0 


1.7 


! 


4.5 


3.9 


l 


8.0 


6.9 


2 


2 8.0 


2 3.4 


3 


6 0.0 


5 1.7 


4 


10 8.1 


9 1.8 


5 


16 8.1 


14 3.5 


6 


24 0.1 


20 7.0 


7 


32 8.2 


28 2 


8 


42 8.3 


36 7.1 


9 


54 0.3 


46 3.7 


10 


66 8.4 


57 2.1 


11 


80 8.5 


69 2.1 


12 


96 0.6 


82 3.9 


13 


112 8.6 


96 7.4 


14 


130 8.8 


112 0.7 


15 


150 0.9 


128 7.6 


16 


170 9.0 


147 2.3 


17 


192 9.2 


165 2.7 


18 


216 1.3 


185 2.8 


19 


240 9.4 


206 4.7 


20 


266 9.6 


228 8.2 



ON LEVELLING. 



31 



Table of the Difference of the Apparent and True Level for 
Distances in Chains. 



Distance 
in 


CORRECTION. 


Curvature in decimals 


Curvature and Refraction in 


Chains. 


of feet. 


decimals of feet. 


1 


.000104 


.000089 


2 


.000417 


.0003,8 


3 


.000938 


.000804 


4 


.001668 


.001430 


5 


.002605 


.002233 


6 


.003752 


.003216 


7 


.005107 


.004378 


8 


.006670 


.005717 


9 


.008442 


.007236 


10 


.010422 


.008933 


11 


.012610 


.010809 


12 


.015007 


.012863 


13 


.017613 


.015097 


14 


.020427 


.017509 


15 


.023450 


.020100 


16 


.026680 


.022869 


17 


.030120 


.025817 


18 


.033767 


.028943 


19 


.037623 


.032248 


20 


.041687 


.035732 


21 


.045960 


.039394 


22 


.050*42 


.043236 


23 


.055132 


.047259 


24 


.060031 


.051455 


25 


.065137 


.055832 


26 


.070452 


.060388 


27 


.0^5975 


.065121 


28 


.081708 


.070036 


29 


.087648 


.075127 


30 


.093798 


.080399 



14 A TREATISE 

The correction for distances greater than those given 
in the latter Table may be computed by the following 
rule, the same by which the Table itself was com- 
puted : 

Rule. — To the arithmetical complement of the logarithm 
of the diameter of the earth, or 2.3788603, add double 
the logarithm of the distance in feet, the sum will be the 
logarithm of the correction for curvature in feet and 
decimals ; from which if one- seventh of itself be sub- 
tracted, the result will be the combined correction for cur- 
vature and refraction. 

The practice of levelling is one of the most delicate 
operations that fall within the province of a surveyor, 
requiring the utmost possible circumspection to avoid 
the numerous sources of error to which he is liable. 
More especially, as it is seldom possible for him, after 
levelling over a long tract of country, to conjecture in 
what portion of the work his error lies, if he should 
then find that he had been so unfortunate as to commit 
any, and, not unfrequently in such cases, sufficient time 
cannot be spared to go over the ground again ; as, for 
instance, when a section is required within a very limited 
time to produce before a Parliamentary committee, 
either to support or oppose any measure submitted to 
their consideration. We have witnessed an instance 
where such a committee, during their inquiry into the 
merits of a certain proposed line of railroad, had 
brought before them a rival contemplated line wixh pre- 
tensions to great superiority ; but it had been so hastily 



ON LEVELLING. 15 

surveyed, that the learned counsel who had the sup- 
porting of the measure, acknowledged, in his opening 
address, that a trifling error at some unknown part of 
the line had been detected, which did not exceed fifty 
feet. We hardly need add, that the rival line was 
rejected. 

The importance of extreme accuracy may also be 
felt, when it is known that from the section, the 
engineer has to make his calculations of the quantity of 
earthwork, in cuttings and embankments, necessary to 
carry into execution the intended measure, whether of 
a canal, a railway, or turnpike road, and of course the 
accuracy of the estimated expense is involved in it ; 
and further, the fitness of the ground itself for such 
works is determined from the section ; that is, whether 
the inclinations, which the undulations of the ground 
admit of being introduced, are suitable for the purpose 
either of a railway or turnpike road. And if the ob- 
ject be the formation of a canal, the section must show 
what extent of lockage will be required ; not only 
affording a key to the expense, but also the possibility 
of its execution. We do not throw out these sugges- 
tions to alarm the mind of the young beginner, by 
bringing before him a fearful responsibility, but that he 
may understand the ultimate object of his labors, and 
to induce him, by carefulness and attention, to merit 
that confidence which is sure to be reposed in those 
who are known to possess such habits. 



16 A TREATISE 



LEVELLING INSTRUMENTS. 

It is essential to the good execution of work, that 
the surveyor should possess instruments most proper 
for the purpose, and of the best construction. Upon 
the subject of instruments, we shall generally refer the 
reader to a cheap work, entitled, " A Treatise on the 
principal Mathematical Instruments employed in Sur- 
veying, Levelling, and Astronomy, explaining their 
construction, adjustments, and use f where the various 
kinds of spirit-levels, and levelling staves, together 
with the method of performing their several adjust- 
ments, &c, are minutely detailed, and represented by 
engravings f and as the work alluded to contains also 
a similar account of the most important instruments 
used in surveying and astronomy, and has had an ex- 
tensive sale, we presume it to be in the hands of most 
beginners in the profession ; we shall, however, give 
some particulars in this place, and annex a description 
of the cause of, and a remedy for, the parallax between 
the wires of a levelling telescope, and the levelling 
staves, which is the cause of much annoyance to 
observers. 

SPIRIT LEVELS. 

The Y level, so called from the supports in which the 
telescope rests, resembling in shape the letter Y, is the 

* Also a work published by Mr. Weale, on Drawing Instruments, with 
Instructions for Field Work, in 12mo, price 3s. 6d. 



ON LEVELLING. 17 

oldest construction of the spirit-level now in use ; its 
adjustments are convenient to be performed, but, on 
the other hand, this kind of instrument seldom retains 
its adjustments perfect for any length of time ; besides, 
there are conditions in its construction which are 
assumed to be perfect, but which practical men know to 
present difficulties in the manufacture. The use of this 
instrument is now very much superseded by those of 
modern construction. 

Troughtorfs Improved Level. — This instrument, has 
been a very general favorite among engineers for a 
length of time ; its construction renders its adjustments 
much more permanent than those of the Y level, and it 
is altogether a more stable instrument. The telescope, 
which , in the former instrument, is capable of rever- 
sion on its supports, for the adjustment of the line of 
collimation, is, in Troughton's construction, firmly fixed 
in its place, as is also the glass tube of the spirit bubble. 
The verification and correction of the adjustments are 
performed very differently, and may at first appear 
more complex and difficult than those of the other ; yet 
when a person has once mastered and become familiar 
with his instrument, these apparent difficulties vanish. 
The Dumpy Level. — This modification of the spirit- 
level has but recently been introduced by William 
Gravatt, Esq., and bids fair to become the favorite in- 
strument among civil engineers. In its general figure 
it does not differ very essentially from the level last 
spoken of, but it possesses many decided advantages. 



18 A TREATISE 

The aperture of the object glass is much larger for the 
same length of telescope ; consequently more rays of 
light are admitted to the eye, producing the advantages 
of greater distinctness. We lately tried a fourteen- 
inch level, constructed upon Mr. Gravatt's principle, 
and found that we could distinctly read the levelling- 
staff at twenty chains (a quarter of a mile) distant, 
which was the utmost we could do with a twenty-inch 
level upon the old construction ; we have, therefore, the 
advantage of a more portable instrument, fourteen 
inches in length, capable of performing the same work 
as a more cumbersome one of twenty inches. Besides 
this advantage, the instrument in question is more com- 
plete in its details. It possesses a cross level, placed 
at right angles to the principal level, which affords very 
great facility in setting up the instrument, and adjust- 
ing for observation, as will be hereafter described ; it 
likewise has a reflecting mirror, mounted with a hinge 
joint, and capable of being placed on the principal level 
tube and adjusted, to show the observer if the instru- 
ment shifts from its liorizontality whilst he is noting 
the observation ; it also possesses other important 
though minor additions, all of which, in fact, could be 
applied by the maker to the other kind of instruments, 
if ordered, and for the particulars of which we refer 
to the work before alluded to. 

From the large aperture and short focal length of the 
telescope, the instrument has altogether a dumpy ap- 
pearance, and hence it is generally known by the cog- 



ON LEVELLING. 19 

nomen of " Gravatt's Dumpy Level f usually of nine 
or fourteen inches. We have seen some beautiful spe- 
cimens of this kind of levelling instrument constructed 
for I. K. Brunei, Esq. 

LEVELLING STAVES. 

In the Treatise on Mathematical Instruments will be 
found a description of the different kinds of levelling 
staves in use. The former construction, even as im- 
proved by Troughton, was decidedly defective in prac- 
tice, inasmuch as the staff had to be read off by the 
assistant, who had then to communicate the result to 
the observer ; or, if he was not sufficiently intelligent 
to be intrusted with so responsible a duty, he was 
obliged, after the observation was made, to carry the 
staff to the observer, or wait for him to come and read 
off the height of the vane, and register it in his field- 
book. This occasioned great loss of time and uncer- 
tainty in the results, for the vane on the staff might 
possibly be shifted in the mean time. We remember 
an instance of an ignorant attendant holding the staff 
upside down, which at once introduced an error of 
several feet in the result. To obviate this, a new staff 
has been contrived, originally, we believe, by Mr. 
Gravatt, and subsequently by Mr. Hennett, Mr. Bra- 
mah, Mr. Sop with, &c, each varying the mechanical 
arrangements, but all agreeing in retaining the main 
advantage, viz., a sufficiently distinct graduated face for 
the observer to read off the quantities himself through 



20 A TREATISE 

the telescope of his instrument ; the sliding vane is 
therefore dispensed with, and the only dependence to 
be placed on the staff-holder is, that he may hold it 
perpendicularly. To assist him in this, a small plum- 
met is suspended in a groove cut out in the side of the 
staff, by which its verticality can be determined in one 
direction, and the observer himself can detect if it be 
held aslant in the other direction, as may be under- 
stood from the diagram at page 26, which represents the 
staff e as it appears in the field of the telescope, which 
shows objects inverted. If the staff be held perpen- 
dicularly, it will appear between and equally distant 
from each of the two vertical wires c d, fixed in the 
telescope ; consequently, if it be held aslant, it will 
cross the wires obliquely, and any want of verticality 
in the staff will be immediately detected, and the ob- 
server must signal to the staff-man accordingly. The 
advantages from the use of the modern staves, over 
those of the old construction, are so great, especially 
in saving of time, that we have no doubt of their 
general adoption. 

THE IRON TRIPOD. 



ON LEVELLING. 21 

Another instrument of simple construction is repre- 
sented in the preceding figure ; its use is to rest the staff 
upon when held at- any station. By this means the 
staff is sure to be kept on the same spot, and at the 
same height from the ground, while the observer is 
reading the staves both at the back and forward station 
on each side of the spirit-level ; it is at present not 
generally used, but we consider it of more importance 
than is usually attached to it. It consists of a trian- 
gular piece of sheet iron, of about one-tenth of an inch 
in thickness, having the corners turned down to form 
the feet of the tripod, which are to be pressed into the 
ground by the foot of the staff-holder ; a rounded- 
piece of iron is riveted on the upper surface, to present 
a clean spot to rest the staff upon when held at the 
station ; the chain with the attached ring is for the: 
convenience of the staff-holder in lifting it from the 
ground, and carrying it from station to station.. 

THE MEASURING CHAIN. 

In levelling operations it is in most cases necessary 
to note the relative distances of the staves from each 
other, from the spirit-level, or from some given point 
or place, otherwise no section of the ground levelled 
over can be made. For this purpose a measuring tape 
may be employed where the distances are short, but in 
most cases the means employed is a chain ; the one 
commonly used is 4 poles in length, called Grunter's 

2 



22 A TREATISE 

chain, which is divided into 100 links of 7.92 inches 
each. In many cases, however, this will not be found 
so convenient as the use of a chain with links of 1 foot 
in length ; but there is a practical inconvenience at- 
tending these long links where the ground is rough and 
uneven, as the links are likely to get bent in being 
drawn through the hedges and rough places ; whenever 
this occurs the chain is reduced in length, and, unless 
discovered and rectified, a considerable error in distance 
will very soon result. When we have had occasion to 
use such a chain over rough ground we have had the 
links made 6 inches long, and although it occasioned 
more trouble in noting and registering the distances, 
yet the liability of the links to become bent was greatly 
diminished. No measurements are required in taking 
what are called running or check levels, the object of 
which is merely to test the accuracy of a section pre- 
viously made, by finding the difference of level between 
certain points on the section, to see if the results are 
identical with the former determination ; which is the 
same thing as acertaining the whole difference of level 
between distant places. Neither are any measure- 
ments required to produce a section if you possess a 
correct map or plan of the district or line, for if the 
level points are noted on the said plan, their relative 
distances can be taken therefrom by its scale ; this, 
however, can only be considered as an approximate 
operation as far as the horizontal measures are con- 
cerned. In this way, however, many extensive trial 



ON LEVELLING. 23 

sections for long lines of railway have been made by 
means of the Ordnance maps, and will, if properly 
done, determine the general features of the country 
sufficiently for the engineer to choose the best route for 
a minute and detailed survey, which would cost too 
much time and money to undertake in the first instance 
where there exists any doubt between two or more 
routes as to which it would be most judicious to adopt. 



ON INSTRUMENTAL PARALLAX. 

The foregoing is an account of the instruments neces- 
sary for the purposes of levelling ; but before closing 
this part of our subject, we think it may be useful to 
add some particulars respecting instrumental parallax, 
which we have occasionally found to be the source of 
much annoyance to the surveyor. This has invariably 
arisen from ignorance of the principles of the telescope, 
and hence, not knowing how the parallax arises, the 
means of removing it have not been understood ; we 
shall endeavor to explain, in a popular manner, both 
the cause and the remedy. 

The rays of light which proceed from surrounding 
objects, and which, by entering our eyes, convey to us 
the sense of vision, move in perfectly straight lines, 
unless turned from their rectilineal course by the inter- 
vention of a refracting or reflecting medium, and what- 
ever portion of such rays as can enter our eyes may 
(without sensible error) be considered as moving not 



24 A TREATISE 

only in straight, but parallel lines ; the more remote the 
object is, the more nearly this will be the case. In the 
adjoining diagram, let A B represent the section of a 




lens (or object glass of a telescope) ; let the parallel 
lines on the left represent the rays of light coming from 
some distant object in that direction • the instant they 
impinge upon the glass, and in passing through it, they 
suffer refraction — that is, they are bent out of their 
former rectilineal path — and on leaving the lens at the 
opposite side, they converge to a certain point D, 
which is the focus of the object glass (in this point all 
the rays passing through a perfectly formed glass meet, 
and it is situated on the line C D, the direction of the 
ray which passes through the centre of the glass, the 
only one that continues its former course, and is called 
the axis of the lens) ; the concentration of the rays 
form an image of the distant object in the focal point 
D, " and if a piece of ground glass, transparent paper, 
or a plate of glass having one surface covered with a 
dried film of skimmed milk, be held up at D, a person 
looking at it from a few inches behind would see a per- 
fect image of the distant object formed on the ground 
glass ; and by steadily keeping the eye in the same 
position, the ground glass may be removed, and the 
image will appear in the same spot suspended in the 



air." 



ON LEVELLING. 25 

Now let us imagine the lens applied to the construc- 
tion of a telescope, and the adjoining diagram to re- 
present a section of it ; the image of a levelling staff 
held at a distance, in the direction of C, would be 
formed at the point W, the focus of the object glass ; 
let D F represent the eye-glass, which is fixed in a slid- 
ing tube, and together called the eye-piece. The eye- 
piece may be considered as a microscope, with which 




the observer magnifies the image of the object formed 
at W ; to do this, it will readily appear to the reader 
that its distance from the image at W must be such as 
to cause its focal point to coincide therewith, making 
that point the common focus of the two glasses ; for the 
purpose of effecting this, the eye-piece is made to slide 
either in or outwards, and the observer can tell when 
it is at the proper distance, for he will then obtain a 
perfectly distinct view of the object. The axis of the two 
glasses forms a continued straight line C E, which in a 
telescope is technically termed the optical axis of the 
instrument, or line of collimation ; this imaginary line 
is, in levelling telescopes, the zero, from whence the 
readings on the staff are taken. It is therefore necessary 
to represent it by something tangible, that shall at the 
same time not interfere with the rays of light passing 
through the telescope to the eye ; this is done by fixing 



26 



A TREATISE 



across the interior of the telescope very fine wires, or 
threads from a spider's web, so that their intersection may 
not only coincide with the axis C E, but cross it precisely 
at W, the common focus of the two glasses, where the 
image of the staff (or distant object) is formed, and there- 
fore the wires and the staff will appear to an observer as 
one object, or, at least, equally distant from him. The 
following diagram shows the appearance of the wires 
and the staff as seen through an inverting telescope ; 
where a b represents the horizontal wire, c and d two 



*_ Lb 111 i 

V c « i J 



wires placed at right angles to it, and separated so as to 
admit, at usual distances, the staff e to appear between 
them, by which the observer can always tell if the 
staff-man holds it erect in a lateral direction, as before 
explained. The staff is represented as seen at the 
moment of completing an observation ; the horizontal 
cross wire coinciding with the division .20 above 16 feet, 
the staff being read downwards in consequence of its 
apparent inversion ; the reading, therefore, of such an 



ON LEVELLING. 27 

observation, to be entered in the field-book, would be 
16.20 feet. 

The adjustment of the line of collimation consists in 
making the centre of the horizontal wire (or intersec- 
tion of the wires in instruments intended for measuring 
angles) coincide with the optical axis of the telescope ; 
this, when once accomplished, will, with care, keep cor- 
rect for a long time, but the placing it in the common 
focus of the two glasses requires attention at every 
observation. For detailed instructions upon the former, 
we refer to the treatise on Mathematical Instruments, 
<fec. ; but as the latter forms part of every observation, 
and is the source of the perplexing parallax, we shall 
speak of it in this place. 

The cross wires are fixed to a plate, called a dia- 
phragm , attachedby screws to the slide G H, which also 
carries the slide D F of the eye-piece. The point W, 
or focus of the object glass, does not remain constant 
for terrestrial objects, but varies with every change in 
the distance of the staff; if it be brought closer to the 
instrument, the image, or focal point, will recede fur- 
ther from the glass, and vice versa ; therefore, the wires 
and the focus of the eye-piece must be brought to co- 
incide with that of the object glass by their respective 
slides ; and first, the eye-piece should be moved in 
its slide till its focus coincides with the wires in the 
tube G H ; when this is accomplished, the observer 
will see the wires perfectly sharp and well-defined ; 
next, motion must be given to the slide G H, by turn- 



28 A TREATISE 

ing a milled head attached to the telescope, which gives 
motion to the slide by rack work ; this will carry both 
the wires and the focus of the already adjusted eye- 
piece to coinc de with the focus of the object glass, on 
whatever part of the optical axis of the instrument it 
may be situated. When this is done, the adjustment 
of the telescope for observation will be complete, and 
its proof consists in the observer having at the same 
time a clear and well-defined image both of the staff 
and the cross wires, which will be the case if they seem 
to be attached to each other, or, in other words, appear 
equally distant from him ; and the moving about of 
the observer's eye does not detect any apparent dis- 
placement of the staff, with respect to the wires. Such 
a displacement, or relative motion, is what is meant 
by parallax ; and when it exists, it must be got rid of 
by a repetition of the adjustment of the glasses as 
above described, till the motion of the eye will no 
longer detect the least apparent movement, or passing 
and repassing of the wires and the staff ; till this is 
done, no correct observation can be made. 



From what has been advanced on the subject of the 
corrections for curvature and refraction, it may be 
necessary, before entering upon any practical examples, 
to remark, that such corrections are very seldom ap- 
plied in practice, the observer, by the arrangements of 



ON LEVELLING. 



29 



his operations, doing away in a great degree their in- 
jurious effects, which we will endeavor to explain. 




Suppose it were required to find the difference of 
level between any two points G and H in the preced- 
ing figure ; let A B represent a portion of the earth's 
surface, let C represent the centre, and C Gr, C I and 
C H the radii of the earth. Now a spirit-level being 
set up and adjusted at I, an observer looking through 
the telescope would see objects in the direction of the 
horizontal line D E only, and a staff held upright 
at H would be read off in the point E on the horizontal 
line ; but this point is higher than the true level by the 
distance H E, which is the correction for curvature due 
to the distance I H (see page 9) ; and if that quantity 
be subtracted from the reading of the staff, the remain- 
der will show the difference of level between the points 
I and H. If the same process be gone through by holding 
a staff at Gr, then the difference of level between Gl- 
and I will also be ascertained, which being compared 
with the former difference, will show how much higher 
one of the points Gr or H is above the other ; but it 
must be evident, that if Gr and H be equally distant 



30 A TREATISE 

from I, the horizontal line D E, being a tangent to the 
surface at the middle point I, must cut the staff at D 
on the same level with the point E ; that is, D is 
equal to C E, therefore D and E are level points, being 
equidistant from the centre of the earth ; and if the 
reading of one staff above the ground is greater than 
the reading of the other, the difference will at once 
show the variation of level between the points where 
the staves were held, viz., G- and H ; the effect of 
curvature is thus removed by simply placing the instru- 
ment midway between the station staves. The effects of 
the atmospheric refraction will likewise be done away 
with in the same process, because it will affect both 
observations alike, unless under peculiar circumstances 
of the weather, &c, over which the observer has no 
control. 

The above method of finding differences of level, by 
placing the instrument as near as possible midway 
between the two staves, and noting their readings, is 
the one adopted in practice ; but as it can scarcely ever 
happen, on account of the extent of the work, that one 
placing of the instrument will complete it, a succession 
of similar operations must be performed, as shown in 
the annexed engraving. 




Suppose it were required to find the difference of 
level between the points A and Gr ; a staff is erected at 



ON LEVELLING. 31 

A, the instrument is set up at B, another staff at C, at 
the same distance from B that B is from A. The read- 
ings of the two staves are then noted ; the horizontal 
lines connecting the staves with the instrument repre- 
sent the visual ray or line of sight. The instrument 
is then conveyed to D, and the staff which stood at A 
is now removed to E, the staff C retaining its former 
position, and from being the forward staff at the last 
observation, it is now the back staff ; the readings of 
the two staves are again noted, and the instrument 
removed to F, and the staff C to the point Gr ; the staff 
at E retaining the same position, now becomes in its 
turn the back staff, and so on to the end of the work, 
which may thus be extended many miles ; the differ- 
ence of any two of the readings will show the difference 
of level between the places of the back and forward 
staff ; and the difference between the sum of the back 
sights and the sum of the forward sights will give the 
difference of level between the extreme points ; thus : 

Back sights. Fore sights, 

ft. dec. ft. dec. 

A and C 10.46 11.20 

C " E 11.33 8.00 

E " G 7.42 7.91 

Sums 29.21 27.11 

27.11 

Difference of level 2.10 

showing that the point G is 2 feet and y 1 ^- higher than 
the point A. 



A TREATISE 



The foregoing process is called compound levelling. 
The following is an example of simple levelling, being 
performed at one operation, and therefore subject to 
the correction for curvature and refraction to obtain a 
correct result. 




Suppose it were required to drain a pond and marsh 
A, by making a cut to a stream at B, a distance of 
thirty chains ; let a level be set up at C, and directed 
to a staff held upright at the edge of the water at B. 
The horizontal line C D represents the line of sight 
which would cut the staff at D, the reading being 17.44 
feet ; the height of the instrument above the ground 
was 4 feet, and the depth of the pond 10 feet ; there- 
fore the difference of level between the bottom of the 
pond and the surface of the stream was as follows : 

ft. dec. 

Beading of the staff. 17.44 

Height of instrument 4.00 

Depth of pond 10.00 

Curvature and refraction for 30 chains 

(see Tables, pages 12 and 13) 0.09 

14.09 

Difference of level 3.35 



ON LEVELLING. S3 



PART II. 
THE PEACTICE OF LEVELLING. 



ON RUNNING OR CHECK LEVELS. 

To present, in the clearest possible manner, the 
practical application of the principles of levelling, we 
propose describing some operations in detail. We 
shall, therefore, commence with a case of a simple 
kind, which will prepare the way for more complicated 
examples. When a section of a line of country has 
been completed (for any purposes whatever), it is in 
most cases necessary to check its accuracy by repeti- 
tion ; but in doing this, it is seldom requisite to level 
over precisely the same line of ground, unless there is 
cause to suspect its general correctness, but to follow 
the most convenient and nearest route, and at intervals 
to level to some known points on the exact line of sec- 
tion, which will give their differences of level ; the 
points thus selected are generally what are called 
bench marks, and are nothing more than marks or 
notches cut upon gateposts, stumps of trees, mile or 
boundary stones, or any similarly immovable objects, 
contiguous to the line of section, and at frequent inter- 
vals. These bench marks are made by the person who 
takes the section in the first instance, and are some- 



34 A TREATISE 

times previously determined upon. When the section 
is complete, their relative heights with regard to the 
base line or datum of the section become known ; con- 
sequently, they may be considered as so many zero or 
fixed points on the line, easily recognizable, from 
whence any portion of the work may be levelled over 
again ; or branch lines of level may be conducted in 
any direction, and the levels of such branches be com- 
parable with those of the main line. 

When, in checking the principal levels, by proceed- 
ing in the most convenient direction from bench mark 
to bench mark, it is found that the differences of level 
prove identical with those on the section , or within 
the limits of probable error, it may be presumed that 
all the intermediate heights are likewise correct ; it is, 
however, just possible that equal errors of an opposite 
kind may have been committed, when, the sum of each 
being of the same magnitude, a balance of errors would 
cause the extreme points to be right, whilst the inter- 
mediate levels would be incorrect ; but the probability 
is so much against such an occurrence, that we believe, 
unless there be some particular reasons for so doing, 
the whole exact line of a section is seldom levelled a 
second time for the purpose of checking the former 
results only. 

From what has been remarked, it will appear evi- 
dent that in taking running or check levels, there is no 
necessity for the use of the chain, or the compass 
attached to the instrument, the distances and bearings 



ON LEVELLING. 35 

having all been determined at the time the principal 
levels were taken. 

The example we are about to give of this kind of 
operation is represented in the engraving, Plate I., 
which shows both the ground plan and the section. 
The strong black line on the plan is that of the section 
to be checked, and proceeds from a bridge in the town 
of A, in a circuitous direction along a valley, and 
nearly parallel to the course of a river, to a bench 
mark in the town of B ; this originally formed a por- 
tion of a more extensive survey. We have selected 
this portion of the line as explanatory of our present 
subject ; the route taken in proving the work is repre- 
sented by the dotted line, and was confined to the 
public roads, that being considered the most convenient, 
because it would altogether exclude the necessity of 
passing through private property, as the surveyor 
would most likely have been ordered off, a great feel- 
ing of opposition existing among the owners and occu- 
piers of the said lands ; and further, the public road 
crossed the line several times, by which a number of 
intermediate points could be checked. Before giving 
the particulars of this example, we shall explain in 
detail the method of conducting the necessary obser- 
vations. 

In the first instance the staff-holder must place his 
staff on the bench mark from whence the levels are to 
commence. (In the case of our example the staff was 
first placed on a peculiarly shaped stone on the crown 



36 A TREATISE 

of the bridge at A, which could easily be recognized 
from description at any future time, if ever it should 
be necessary to refer to this spot again ; it therefore 
answered as a bench' mark.) The surveyor must next 
set up his spirit-level in the most suitable spot which 
presents itself, from whence he can have an unin- 
terrupted view, not only of the staff at the back station, 
but also for a considerable distance in the direction he 
wishes to carry his levels. The station selected should 
not in any c ase exceed four or five chains, and if it be 
only half that quantity, there will be less likelihood of 
error ; for when long sights (as they are usually 
termed) are taken, unless both the back and forward 
stations are equally distant from the instrument, errors 
will gradually creep in upon the results, which, in a 
long series of levels, are liable, by their accumulation, 
to become of serious consequence. The proper station 
being determined upon,* and the tripod legs of the 
instrument spread out and thrust into the ground suf- 
ficiently to insure its stability, the observer must adjust 
his level for observation in the following order : — 
First, he must draw out the eye-piece of the telescope 
till he sees the cross wires perfectly well defined ; then, 
directing it to the staff, he must turn the milled-headed 
screw, on the side of the telescope, till he can likewise 
distinguish with the utmost possible clearness the 



* It must be borne in mind, when we thus minutely detail what may 
appear to the practical man as naturally obvious, that we are writing for the 
information of those who have never had any practice whatever. 



ON LEVELLING. 37 

smallest graduations on the staff ; that these two 
adjustments be very carefully and completely per- 
formed, is of more consequence than is generally sup- 
posed, for upon them depends the existence or non- 
existence of parallax. If any parallax is detected, it 
must be removed, or the observations will be incorrect ; 
its existence may be detected by the observer moving 
his eye about at the same time that he is looking 
through the telescope at the staff ; and if he sees that 
the cross wires do not appear to have the least motion 
with regard to the divisions with which they are coin- 
cident, then no parallax will exist ; but if any motion 
appears to take place between the wires and the staff, 
it is a proof that one or both of the foregoing adjust- 
ments have been imperfectly made. 

To remedy this inconvenience the eye-piece should 
first be moved to try and improve the distinct appear- 
ance of the cross wires. The observer will be greatly 
assisted in this operation if he holds a sheet of white 
paper before the object glass, which, at the same time 
that it prevents other objects from attracting his atten- 
tion, presents a clean white disk, or ground, for the 
wires to be seen upon ; and when he is satisfied that 
they are as sharp and well-defined as possible, he must 
repeat the movement of the milled head by the side of 
the telescope till he is equally satisfied of the distinct 
appearance of the graduations on the staff ; then let 
him again move his eye about before the eye-glass to 
see if any parallax still exists, and if so, he ought to 

3 



38 A TREATISE 

repeat the above simple operation until it is removed. 
We have known the parallax of a telescope to be a 
source of great annoyance to persons in the profession, 
which has led us to be thus minute upon what to some 
would appear very simple. We have for the like rea- 
son given an explanation of its nature, &c, at page 23. 

The turning the mill head to obtain distinct vision 
of the staff, in the old construction of instruments, 
communicated motion to the object glass ; but in those 
of recent contrivance, it moves the whole of the eye 
end of the telescope, and with it the cross wires. In 
either case, the distance between the object glass and 
the wires is increased to a proper extent j the modern 
contrivance appears to be the most approved. The 
adjustment of the eye-piece for distinct vision when 
once made, is not likely to require alteration the whole 
day, unless it be accidentally deranged ; but that of 
obtaining distinct vision of the distant staff (together 
with the one we shall next describe) must be performed 
at every station, as it varies with the distance of the 
staff, as explained at page 27. 

Having made the above adjustments perfect, bring 
the spirit-bubble into the centre of its glass tube, which 
position it must retain unmoved in every direction of 
the instrument j or, in other words, the bubble must 
indicate a true level during the time the telescope is 
turned completely round horizontally on its staff head; 
this is accomplished by bringing the telescope succes- 
sively over each pair of the parallel plate screws, and 



ON LEVELLING. 39 

giving them motion, screwing up one while unscrewing 
the other to a corresponding extent ; but if the tele- 
scope is supplied with a cross level, as in that con- 
trived by Mr. Gravatt, the two bubbles, being at right 
angles to each other, will at once show which pair of 
screws require turning, in order to produce an indica- 
tion of level in both bubbles. In the Treatise on 
Mathematical Instruments there is given an ample ex- 
planation of the adjustment of levels in all their details; 
upon such subjects we shall once for all refer to that 
work. 

Having adjusted the level for observation, it must be 
directed to the back staff, of which a clear view must 
be had ; then note with all possible exactness the foot, 
and decimal fraction of a foot, with which the central 
part of the horizontal wire appears to be coincident, 
which enter in the proper column of the field or ob- 
servation book. This column should be headed ' ' Back 
Sight," or " Back Station, 77 as in the example given at 
page 45. As soon as it is registered, look to see that 
the spirit-bubble has not removed from its central 
position, and then repeat the observation, to insure 
that no mistake had been made in noting it ; this should 
be invariably done, to guard against errors. 

The back observation being made, turn the telescope 
round in the forward direction, and obtain a distinct 
view of the staff, by turning the milled head at the side 
of the telescope ; then look at the spirit-bubble, and if 
it has at all changed its position, by receding towards 



40 A TKEATISE 

either end of its tube, bring it back to the centre by 
the parallel plate screws, as before described (this can 
be done so readily, and without moving the telescope, 
when a cross level is attached, and having likewise 
other advantages, that we recommend its universal 
application to spirit-levels) ; then, by looking through 
the telescope, observe what division on the staff is in- 
tersected by the cross wire, and enter the reading in 
the proper column of the field-book, which should be 
headed "Fore Sight,"' or "Fore Station." Having 
entered it, look to see that the bubble is still correct, 
and then verify the observation by noting it again, 
which will complete the first levels.* 

It may be worth remarking that, in setting the level 
up, the pointed legs should be pushed into the ground 
sufficiently to insure the stability of the instrument, 
and likewise that the observer should move himself 
about the instrument, whilst taking the levels, as little 
as possible, taking care not to strike the legs with his 
feet. Caution in these matters is required, for some- 
times the least movement of the person will derange 
the levels of the instrument, particularly on loose or 
elastic ground ; to do away the inconvenience arising 
from this source, a reflector has been contrived to fix 
on the top of the telescope tube, by which the observer 
can see both the staff and the reflected image of the 

* When taking levels for the formation of a section, it is sometimes neces- 
sary to note the bearing of the compass needle, and to measure distances, as 
will be explained hereafter. 



ON LEVELLING. 41 

spirit-bubble at the same time, and then he can make 
his observation at the instant he sees the bubble in its 
proper position. The foregoing description of the 
method of taking levels is general, and applies equally 
to every kind of levelling operation, with whatever 
additional matters may require attending to, when 
taking levels for the formation of a section, &c, which 
we shall hereafter describe. 

The first levels being completed, the surveyor must 
take up his instrument, and, passing the man who holds 
the forward staff, proceed to some convenient spot to 
set up the instrument a second time, which, as before 
remarked, should not be more than four or five chains 
distant ; the other man, also, who held the staff at the 
back station, must likewise take up a new station still 
further onwards in the required direction, and as nearly 
as possible at the same distance from the instrument as 
the instrument is from the staff, which has now become 
the back station ; it being in every case necessary, to 
insure correct work, that the instrument should occupy 
very nearly the middle point between the staves, for 
reasons which will be understood by those who have 
perused the former part of this book. Having set the 
instrument up, adjust it for observation as before, viz., 
see that the cross wires are distinct ; turn the milled 
head by the side of the telescope till the graduation on 
the staff is quite distinct, and no parallax exists ; and, 
lastly, set the spirit-bubble level in every direction of 
the telescope by the parallel plate screws ; which done, 



42 A TREATISE 

note the reading on the back staff, and enter it in the 
book ; then examine the bubble, and again read the 
staff to insure accuracy ; then turn the telescope about, 
and do the same for the forward station, which will 
complete the second level. As the third and fourth, 
and all the following levels are conducted in precisely 
the same manner, it will be unnecessary to repeat the 
instructions again. 

The man holding the back staff should be instructed 
never to move it in the least from its position till the 
forward observation is completed, which he can always 
tell by seeing the surveyor carry his level onwards. 
It is sometimes the practice to use one staff only, and 
after taking the back observation, to cause the assistant 
to go on and take up a position suitable for a forward 
station ; but besides the loss of time attendant upon 
such a process, if the instrument should in the interval 
get moved by accident, those two observations will be 
incorrect, unless the back sight be taken again, and 
this cannot be done unless the precise spot before 
occupied by the staff can be identified, which is some- 
times uncertain. When this is the case, no alternative 
is left but to go back and renew the work at the last 
bench mark, or known station ; and if none such exist, 
the whole operation will probably have to be gone 
over again, where great accuracy is required. 

The iron tripod, described at page 20, should in all 
cases be placed on the ground by the staff-holder, to 
rest the staff upon, as it insures to the observer the 






ON LEVELLING. 43 

certainty of the staff keeping exactly the same spot 
when the face of it is presented to him in the two 
directions, forward and backward. The staff-holder 
should likewise be instructed to hold the staff perfectly 
upright, which he can himself determine, in one direc- 
tion, by a little plumb-weight suspended in a groove 
in the staff ; and as the observer can tell if he holds it 
upright in a lateral direction (as explained at page 20), 
he should' frequently look to see if he signals for him 
to move the upper end of the staff to the right or left, 
taking care not to disturb its position on the iron 
tripod. 

We have been supposing the use of the newly intro- 
duced staves, as we do not expect that those of the 
former construction will hold their ground against 
them, they having the advantage of providing to the 
observer the means of noting the reading of the staff 
himself. If, however, from habit or otherwise, the use 
of the staff with the sliding vane should be preferred, 
the foregoing instructions equally apply ; the only dif- 
ference in its use is, that the observer must signal to 
the staff-holder to move the vane up or down on the 
staff, till it appears bisected by the cross wires of his 
telescope ; then the reading of the staff must be noted, 
and entered by the assistant in a temporary book car- 
ried by him for the purpose ; or if he cannot be trusted 
to perform so important a part of the business, he must 
convey the staff to the observer, or wait for him to 
come and read it himself. It requires no comment to 



44 A TREATISE 

show the uncertainty, and loss of time, in this method 
of proceeding compared with the use of the newly- 
contrived staves. 

Having explained the method of taking observations 
for checking levels, we must refer to our example. 
The levels, as before stated, were taken along the 
public road shown by the dotted line, that being the 
most convenient route from the town of A to the town 
of B, avoiding the necessity of passing through private 
property ; the strong black line on the plan shows 
where the original section was taken ; the section itself 
is represented above the plan, and is drawn to two 
scales ; the one giving the horizontal measure, is the 
same as that of the plan, viz., one inch to one mile ; 
and the vertical scale, i inch to 100 feet ; from this 
section it appears that the crown of the bridge at A is 
fourteen feet above the datum line D E of the section, 
and that the bench mark (a stone by the road side) at 
B is 111 feet above the same datum ; therefore the 
difference of level between the two places is 111 — 14 
= 97 feet. Now, by referring to our observation book, 
of which we have subjoined a copy, we make the dif- 
ference of level to be 96.8 feet, differing from the 
original section no more than two- tenths of a foot, or 
2.4 inches, a quantity that may be disregarded ; the 
inference, therefore, to be drawn from such a coincid- 
ence in the two results is, that the whole of the section 
between the points in question is sufficiently correct. 



ON LEVELLING. 



45 



Copy of Field-Book, for running or check levels. 



Back 
Sights, 


Fore 
Sights. 


Remarks. 


0.34 


3.16 


Back on B. M. on the bridge at A. 


5.86 


5.61 




4.19 


4.24 


Forward 6 at corner of road leading to B. 


5.44 


1.20 




4.96 


3.20 




4.73 


1.32 


At crossing of line. 


6.10 


2.00 




5.33 


3.96 




5.91 


1.83 




5.70 


0.90 




6.02 


1.21 


Staff placed on post notched for B. M. 


1.21 


4.00 


At crossing of line. 


3.53 


6.07 




3.96 


5.34 




3.94 


4.81 




3.98 


6.08 




4.08 


4.94 


Upon line. 


3.90 


3.96 




4.84 


2.42 




1.54 


5.12 




4.69 


4.97 




5.04 


1.60 




2.24 


3.86 


Upon line. 


7.25 


1.89 




4.03 


1.30 




9.54 


0.19 




6.70 


1.70 




9.40 


4.06 




6.44 


0.38 




11.00 


0.46 




5.98 


1.30 




11.12 


1.78 




9.84 


2.20 




0.18 


0.32 


Upon line. 


4.72 


0.10 




8.89 


0.77 




10.02 


0.92 




10.00 


1.03 




8.58 


1.19 




9.53 


1.18 


Sums. 


230.75 


102.57 


102.57 




Difference. 


128.18 





46 



A TREATISE 



Copy of Field-Book — continued. 



Back 

Sights. 


Fore 
Sights. 


Remarks. 


128.18 




Brought forward. 


9.90 


0.68 




9.04 


0.35 




10.00 


8.52 




3.00 


11.55 




3.68 


0.88 




7.21 


8.75 




1.99 


10.48 




0.65 


10.00 




4.48 


10.44 




1.47 


10.30 * 




1.55 


11.70 




2.45 


9.88 




3.78 


1.04 




6.64 


2.65 


Forward 6 on B. M. called B. 
Sums. 


194.02 


97.22 


97.22 




Differ en ce=dif. of level betw'n A and B. 


96.80 





The back sights being greater in amount than the 
forward sights, it is evident that the bench mark at B 
was higher than the bench mark at A by the difference 
of the two sums. 



LEVELS FOR THE FORMATION OF A SECTION. 

Next to the running levels, the most simple case 
that can occur is, to take the levels of a line of country 
where the ground plan is already made, and the exact 
line of section determined upon, and in some instances 
picketed out. It is then only necessary, in addition to 
what is required for running levels, that the distance 



ON LEVELLING. 47 

between the levelling staves, or the whole distance at 
every station from the starting point, be measured. 
The instrument should be placed, as usual, as near as 
can be at an equal distance from each staff; but it is 
not essential that it be placed in the exact line between 
them, unless it should happen to prove the most ad- 
vantageous position. Plate II. represents an example 
of this kind of work, the survey of the land having been 
completed, and the plans of the fields, etc. drawn ; the 
strong black line A B was the direction determined upon 
as the most suitable for a portion of an intended line of 
railroad, and the section was accordingly taken ; a bench 
mark had been previously agreed upon at each extremity 
(A and B), from whence other surveyors could take up 
the levels, and carry them onwards in both directions. 

First, a staff was placed on the bench mark at A for a 
back station, and another staff was held up for a forward 
station, in the adjoining field, but exactly on the line 
as marked down on the plan, a copy of which the sur- 
veyor had in his possession ; the instrument was then 
set up, as near as could be estimated, or the level of 
the ground would admit, at an equal distance from each 
staff, so as to be able to read them both ; the adjustment 
of the instrument for observation, as described at page 
35, was carefully attended to ; and the reading of the 
staves noted. As soon as the observations were made, 
the distance from staff to staff was measured with a 
Gunter's chain, which completed the first level. 

The measurement of the distances can be more con- 



48 A TREATISE 

veniently performed, and with a great saving of time, 
by two additional assistants, who can be measuring, 
whilst the surveyor proceeds to direct the man who held 
the back staff in the last case, to take up a forward 
station precisely on the line as laid down on the plan. 
The staff which was the forward station in the last case 
now becomes the back station, and the instrument must 
be set up so as to read both stations as before, and as 
nearly equidistant from them as can be ; by the time 
the instrument is adjusted, and both the staves read off, 
the assistants would have completed the measurement 
from the bench mark A to the first forward staff, and 
be ready to continue on to the second one ; whilst this 
is doing, the instrument and back staff can be carried 
forward and set up, &c, as before ; by a continued 
repetition of a similar process, the whole line A B was 
levelled. 

The measuring assistant should report to the surveyor 
the total distance of each forward staff from the bench 
mark at A as soon as it is determined, or, if thought 
more convenient, he may keep a book to enter the 
distances in, which should be ruled in two columns, one 
for his distances, and the other for references to them; 
as a, b, c, etc., or the numbers 1, 2, 3, etc., placed 
opposite ; and if the observer makes similar notes in his 
book to each pair of sights, there can arise no mistake 
in placing the corrreet distances opposite the corre- 
sponding levels, when the measurer makes his return. 

The following is a copy of the field-book of the 



ON LEVELLING. 49 

example given in Plate II. ; showing the manner of 
keeping it, and also the method adopted of reducing the 
levels to obtain the actual heights of each station, with 
regard to the starting point, for the purpose of drawing 
the section ; which we shallthen explain. 



50 



A TREATISE 



LEVELLING FIELD-BOOK. 



Dis- 
tances. 


Rise. 


Back 
Sight. 


Fore 
Sight. 


Fall. 


Reduced 
Level. 


Remarks. 


519 


5.83 


13.71 


7.88 




+ 5.82 




1315 




9.40 


16.30 


6.90 


- 1.07 




1542 




3.87 


11.71 


7.84 


- 8.91 




1850 





2.63 


12.41 


9.78 


- 18.69 


.. 


2358 


13.67 


14.62 


0.95 




- 5.02 




2698 


15.55 


17.00 


1.45 


. . . . . . 


— 10.53 




3357 




10.66 


15.40 


4.74 


+ 5.79 




3758 




2.87 


17.00 


14.13 


- 8.34 




3976 


• • . . . 


3.40 


10.32 


6.92 


-15.26 




5077 


3.49 


5.73 


2.24 




- 11.77 




5904 


15.69 


16.54 


0.85 




— 3.92 




6124 


15.19 


16.08 


0.89 




— 19.11 




6437 


13.83 


14.56 


0.73 




-f- 32.94 




7467 




10.36 


14.06 


3.70 


-- 29.24 




8369 


8.48 


9.84 


1.36 




— 37.72 




9303 


2.80 


9.80 


7.00 




— 40.52 


j Centre of road at 215 
j links. 






2.30 


10.96 


8.66 


— 31.86 


9679 




10.96 


14.46 


3.50 


- 28.36 




9936 




2.08 


15.05 


12.97 


-f 15.39 




10164 




1.75 


16.58 


14.83 


-j- 0.56 




10576 
11423 




1.84 
0.00 


17.10 
7.43 


15.26 
7.43 


- 14.70 

- 22.13 


j Forward at corner 
"j of Wood. 


13066 


1.88 


5.38 


3.50 




— 26.25 


14954 


4.00 


8.50 


4.50 




- 16.25 




15650 


3.94 


5.30 


1.36 




- 12.31 




17345 


0.80 


10.20 


9.40 




- 11,51 




19135 


6.46 


6.86 


0.40 




- 5.05 




19359 


7.04 


11.00 


3.96 




- 1.99 




19631 


8.27 


11.80 


3.53 




-10.26 




19841 


7.85 


10.53 


2.68 




f 18.11 


j Forward e at edge of 
"1 Wood. 


20561 


6.84 


8.22 


1.38 




-24.95 


21671 


6.56 


8.76 


2.20 




-t- 31.51 








14.00 


14.50 


6.50 - 


-31.01 


Road at 450 links. 


22710 


10.18 


14.50 


4.32 




-41.19 




23221 

Sums. 


8.14 


9.14 


1.00 


l_ 
i 


f 49.33 


B above A. 


166.49 304.19 


254.86 


117.16 






117.16 254.86 












49.33 j 49.33 







ON LEVELLING. 51 

The first column contains the measured distances 
from the starting point to every forward station ex- 
pressed in links of Grunter's chain. The two central 
columns, headed "Back Sight" and "Fore Sight," 
contain the readings of the two staves at the back and 
fore observations respectively. The difference of such 
readings is placed in one of the two side columns headed 
" Rise" or "Fall," according as the ground at the for- 
ward station is higher or lower than that at the back 
station. If it be highest (or the ground rises, as it 
is called), then the forward reading will be the smaller 
of the two ; but if it be the lowest (or the ground falls), 
then the forward reading will be the greater of the two ; 
thus, in our first reading, the back observation is 13.71, 
and the forward observation 7.88, their difference^ 
5.83 feet, which is the difference of level between the 
two points ; and as the forward rea^ ing was the smaller 
of the two, it is clear that the ground was rising at that 
place, and therefore the difference of the readings, 
viz. 5.83, is placed in the column of rises. In the next 
three successive pair of sights, the forward readings 
are the greatest, indicating a continued descent of the 
surface line, and the differences of those readings are 
inserted in the column of falls, viz. 6.90, 7.84, and 9.78. 
At the next following sight, the forward reading is 
again the smallest, therefore the difference 13.67 is 
placed in the column headed " Rise," and so on of the 
rest. No mistake can arise by placing the subtraction 
in the wrong column, as in every instance it must be 



52 A TREATISE 

placed in the column adjoining the larger quantity ; 
thus if the fore sight is greater than the back sight, the 
resulting quantity must be placed in the column of falls, 
which is adjoining to that containing the reading of 
the fore sight, and vice versa. 

The adjoining column, headed " Reduced Levels," 
contains the absolute heights of each forward station 
above the datum line of the section, or a horizontal line 
passing through the starting point or bench mark A ; 
these quantities, which are technically called the reduced 
levels, are obtained by the constant addition and sub- 
traction of the numbers contained in the columns of 
"Rise," and "Fall," the former being considered as 
positive, and the latter as negative quantities ; thus, 
assuming the level of the starting point A as the datum, 
we have the first forward station 5.83 feet higher than 
the datum, therefore in the column of reduced levels it 
is marked -f- (plus) ; next we have a fall or negative 
quantity of 6.90 feet, which must be subtracted ; but as 
it is greater than 5.83, it shows that this station is 
below the datum line, by the difference between 5.83 
and 6.90=1.07 feet, which is the depth of the second 
forward station below the datum line, and therefore is 
marked — (minus) ; the next is likewise a fall of 7.84, 
and as our last result was below the datum line, this 
additional negative quantity will take us still lower by 
its whole amount ; it must, therefore, be added to 1.07, 
giving 8.91 feet for the depth of our third forward 
station below our datum, and it is therefore entered in 



ON LEVELLING. 53 

the column of reduced levels with a minus sign. The 
next is also a fall of 9.78, which, applied as the last, 
gives 18.69 for the depth of the fourth forward station 
below the datum. The ground then rises again, and 
we have an ascent of 13.67 feet, which will bring us 
nearer to our datum ; and as it diminishes our depth 
below the datum line it must be subtracted from the 
last result; thus, 18.69 — 13.67 =5.02 feet for the 
depth of the fifth forward station below the datum ; we 
have then a rise of 15.55, which will carry us above the 
datum by the amount of difference between it and 5.02,, 
leaving 10.53 feet for the height of the sixth forward 
station above the datum line ; the next is a fall of 4.74,. 
which diminishes our height by that quantity, and there- 
fore must be subtracted from 10.53, leaving 5.79 as the 
height of the seventh forward station above the datum. 

In like manner every other pair of sights in our 
example was reduced, applying each difference of the 
back and forward readings with their proper signs, until, 
at the close of the work, the point B (the last forward 
station) was found to be 49.33 feet above the datum line, 
or level of the starting point A. 

The reduction of levels becomes a simpler operation 
when the height of the bench mark (used as a starting 
point) above the intended datum line is known ; thus 
(in our example), suppose the height of the bench mark 
A was 100 feet above the level of high- water Trinity 
mark at London Bridge, and that it was intended to 
assume the level of that mark as the datum line of our 

4 



54 A TREATISE 

section ; then^ 5.83 feet, the rise to the first forward 
station, must be added to 100, giving 105.83 for the 
height of the ground at the point a above datum ; next 
from 105.83 subtract the fall 6.90, which gives 98.93 
for the height of the point b above datum ; then from 
98.93 subtract 7.84, which gives 91.09 for the height of 
c above datum ; and in like manner, by adding the 
quantities of rise, and subtracting those of the falls, the 
whole line of levels may be reduced to the line assum- 
ed as the datum. 

As a proof of the accuracy of the arithmetical opera- 
tion, the columns of back and fore sights should be 
added up, and the lesser sum subtracted from the 
former ; the result of the agreement with that by the 
reduced levels is a proof of accuracy. Likewise an- 
other proof may be obtained by adding up the contents 
,of the column of rise and fall ; and if upon taking the 
lesser sum from the greater, the remainder represents 
ithe same quantity as obtained by both the other opera- 
tions, there can be no doubt of the correctness of the 
reductions of the levels, as in our example. By the 
reduced levels, the height of B above A is 49.33 feet. 
The sum of the back readings is 87.95, and that of the 
forward readings 38.62 ; their difference also gives 
49.33 for the height of B above A ; and, lastly, the 
sum of the rises is 54.88, and that of the falls is 5.55, 
the difference giving, as before, 49.33 feet. 

It is, perhaps, to be recommended that the observer 
should reduce his levels as he proceeds in the field, as 



ON LEVELLING. 55 

it will occupy but very little time, and can be frequently 
done while the staff-man is taking a new position ; 
besides, the observer will frequently be able to detect by 
the eye if he is committing any glaring error, as, for 
instance, inserting a number in the column of rises, 
when it ought to occupy a place in that of the falls, the 
surface of the ground at once reminding him that he is 
going down hill instead of ascending. 

If the foregoing method of reducing levels be found 
difficult or troublesome, on account of the introduction 
of plus and minus signs, they can be dispensed with as 
well as the columns of " Kise" and " Fall" by proceed- 
ing in the following manner. Assuming the starting 
point to be any even number of feet high ; or ? what is 
the same thing, assume a datum line any even number 
of feet below the starting point, as 100 or 1000, taking 
care that your choice falls upon a number greater than 
the number of the whole fall you are likely to experience 
in the operation ; then from this assumed height subtract 
the reading of the forward staff, and to the remainder 
add the reading of the back staff ; the result will be the 
height of the first forward station above the assumed 
datum line ; then from this height subtract the next 
forward reading, and to the remainder add the reading 
of the back staff ; the result will be the height of the 
second forward station above the assumed datum, and 
so on throughout the whole levelling operation. The 
difference between any two of the readings will be the 
difference of level between the corresponding points on 
the ground. 



56 



A TREATISE 



By way of illustration, we will reduce part of the 
foregoing example after this manner, and the student 
can adopt whichever method he may consider the best. 



Back 

Sight. 


Fore 
Sight. 


Reduced 
Levels. 


Remarks. 


13.71 


7.88 


100.00 

7.88 


Assumed datum. 

j Height of 1st forward station 
( above assumed datum. 

Height of 2d do. above do. 
3d do. " do. 

4th do " do. 
5th do. " do. 
6th do. " do. 

7th do. " do. 
8th do. " do. 


92.12 
13.71 


9.40 


16.30 


105.83 
16.30 


89.59 
9.40 


3.87 


11.71 


98.93 
11.71 


87.22 

3.87 


2.63 


12.41 


91.09 
12.41 


78.68 
2.63 


14 62 


0.95 


81.31 

0.95 


80.36 
14.62 


17.00 


1.45 


94.98 
1.45 


93.53 

17.00 


10.66 


15.40 


110.53 
15.40 


95.13 

10.66 


2.87 


17.00 


105.79 
17.00 


88.79 

2.87 






91.66 



ON LEVELLING. 57 

The preceding will, we trust, be found sufficient to 
make ourselves understood upon the subject of reducing 
levels. If, after adopting the latter mode, it should be 
required to reduce them to the level of the starting 
point as a datum, nothing more is required than to 
take the difference between the height thus found and 
that of the assumed datum; thus, in our example, sub- 
tracting 100 (the assumed datum) from the height of 
the first forward station, gives 5.83 for its height above 
the starting point ; next, from 100 subtract 98.93=1.07, 
making the second forward station that quantity below 
the level of the starting point, and so of the rest. But 
it may be done much easier after the section is made 
to the assumed datum, by drawing a line parallel there- 
to through the point A, or any other that may be de- 
termined on ; thus the section may be at once adapted 
to any required datum line. 

TO DRAW THE SECTION. 

The levels being reduced, the surface line may be 
represented in the form of a section, as shown above 
the plan in Plate II. The vertical and horizontal 
scales of a section are seldom the same, which produ- 
ces a caricatured representation ; the vertical scale being 
so much greater than the horizontal, shows the depths 
of cutting and embankment required in the execution 
of road, railway, or canal works, with greater clearness 
than if both scales were equal. The plans and sections 
of projected works deposited with the Clerks of the 



58 A TREATISE 

Peace of counties, and in the Private Bill office, to ob- 
tain the sanction of the Legislature, are mostly drawn 
to scales of four inches to one mile horizontal, and one 
hundred feet to one inch vertical ; we have adopted 
these scales in our example, Plate II. 

To make the section of our present example, first 
draw the horizontal line C D as the datum to which our 
levels were reduced, assume any point A as the start- 
ing point, then set off the measured distance from A to 
the first forward station a=519 links (see levelling 
field-book, page 50), at this point erect a perpendicu- 
lar, and mark on it the height 5.83 of the first forward 
station, and connect the point A with this mark, and 
the result will show the surface line of the ground in 
that interval ; next, from the same starting point A set 
off the point b, the second forward station, with the dis- 
tance of 1315 links, as given in the levelling-book ; but 
as this point is a minus quantity (see reduced level, 
page 50), that is, below the datum line, let fall a per- 
pendicular, and set off on it 1.07 feet, which connect by 
a line with the former level, and the surface line from 
A to b will then be represented ; then with the distance 
1542 set off the point c, and on a perpendicular let fall 
therefrom, set off 8.91, which connect as before, and 
the section will be complete from A to c. In like man- 
ner, proceed with the rest of the reduced levels at the 
points d, e,f, &c, till the whole section is drawn. 

Although, for the sake of clearness of description, 
we have desired the person plotting the section to draw 



ON LEVELLING. 59 

the perpendicular, and thereon define the level point of 
the surface as he proceeds with setting off the horizon- 
tal distances step by step, yet in practice he will find it 
most expeditious in the first instance to place the cham- 
fered edge of his ivory scale for the distances along the 
datum line, and at once to prick off the whole of the 
distances (or any convenient portion of them) succes- 
sively as the numbers appear in the field-book ; then 
draw all the perpendiculars by means of a parallel rul- 
er, or by a T square if the paper is properly fixed on a 
drawing table ; and, lastly, from the vertical scale prick 
off all the perpendiculars and connect those points, and 
the section will be made. 

The distances given in the proper column of the 
field-book are supposed to be horizontal distances, and, 
in measuring them, care should be taken that they are 
as nearly such as possible (or they must afterwards be 
reduced thereto), otherwise the section will be longer 
than it ought to be. For the purpose of assisting the 
surveyor in making the necessary reduction from the 
hypothenusal to the horizontal measure, when laying 
down his section, we annex the following Table, show- 
ing the reduction to be made upon each chain's length, 
for the following quantities of rise, as shown by the 
reading of the staves : — 



60 



A TREATISE 



Rise in feet for 


Reduction upon one chain 


one chain. 


in links and decimals. 


1 


0.01 


2 


0.04 


3 


0.11 


4 


0.19 


5 


0.29 


6 


0.44 


7 


0.56 


8 


0.74 


9 


0.94 


10 


1.16 


11 


1.40 


12 


1.76 


13 


2.01 


14 


2.24 


15 


2.61 


16 


2.99 


17 


3.39 


18 


3.76 


19 ' 


4.23 


20 


4.64 



The section can be referred to any other datnm than 
the one by which it was produced ; as, for instance, let 
it be required to refer to section, Plate II., to a datum 
line 100 feet below the point A ; all that is requir- 
ed to be done is, to draw a line E F parallel to C D, at 
100 feet below it ; then, by drawing perpendiculars from 
the surface line to this new datum, as shown by the 
dotted lines, the transfer will be complete, as the height 
of any point can be measured by the scale of the sec- 
tion. We need not go through a further explanation 
of this subject, as an inspection of our engraved exam- 
ple will explain whatever further may be required. 



ON LEVELLING. 61 



WORKING SECTION. 

For the purposes of carrying into execution any 
work, the section should be much more minute than is 
requisite for general purposes ; it is then called a work- 
ing section. The following are the field notes taken 
for such a section, the line having first been carefully 
set out and a stake driven into the ground at the ex- 
tremity of each chain's length : these stakes were about 
18 inches long and 2 inches square (and were furnish- 
ed by a country wheelwright at the price of ten-pence 
per dozen) ; every tenth stake was circular, and some- 
what larger, and had an iron ring round its top, and 
together with every fifth stake had their tops painted 
white, the more easily to identify them ; they were all 
numbered (or considered to be numbered) from one 
end of the line to the other. Plate III. shows the sec- 
tion of the ground and railway at the extreme end of 
the line where the numbers terminate at 1103 chains or 
] 31 miles and 3 chains ; we would recommend the stu- 
dent to plot this section from the notes several times, 
and to various scales, that he may not only better un- 
derstand the subject, ;but also for the sake of practice, 
it being an actual example from the working section of 
a line of railway now completed and opened to the 
public. 



62 



A TREATISE 



FIELD NOTES— Wokking Section. 



Rise. 


Back 
sight. 


Fore 
sight. 


1 

Fall. Distance. 

1 


Reduced 
Levels. 


Remarks. 


feet. 


feet. 


feet. 


feet. 


Links. 


feet. 

270.72 


Brought forward (from 




4.47 


4.53 


0.06103300 270.66 


last page of Notes). 




4.53 


9.22 


4.69103400|265.97 




4.15 9.22 


5.07 




103500 270.12 




4.83 5.07 


0.24 




103600274.95 




4.49 6.36 


1.87 




103700,279.44 




4.67 6.14 


1.47 




103800 284.11 


( Side of clapping post 


4.52 6.62 


2.10 




103900,288.63 


< of field gate in oc- 












( cupation road. 




2.10 


2.24 


0.14K 




0.9510.42 


9.47 






289.44 


f Lower hanging hook 

{ of gate. 

] Centre of occupation 

( road. 

Edge of road. 




9.47 


13.22 


3.75 


103944 


285.69 


0.0713.22 


13.15 




103956 285.76 


4.4013.15 


8.75 


103966 290.16 


Top of bank. 


4.27 8.75 


4.48 




103976294.43 


Do. do. 


0.16 4.48 


4.32 




1040001294.59 




| 2.44 


8.84 


6.40: 1288.19 


B. M. south side of line. 


6.01 8.84 


2.83 


1104100 294.20 






0.74 


2.18 


1.44104200|292.76 






2.18 


5.35 


3.17104300,289.59 






6.77 


7.28 


0.51104400 289.08 




0.03 7.28 


7.25 




104490,289.11 


Edge of ditch. 


| 7.25 


8.36 


1.11 


104492 288.00 


Bottom of ditch. 


4.79 8.36 


3.57 




104500 292.79 


Stump, top of bank. 


0.62 3.37 


2.75 




104600,293.41 




1.32 2.75 


1.43 




104700:294.73 






1.10 


2.25 


1.15104800:293.58 






2.25 


8.86 


6.63104900,286.95 


Enter alder plantation. 




5.65 


9.53 


3.88104920 283.07 






9.53 


11.50 


1.97,105000281.10 




0.33 I 


5.52 


105021281.43 






5.52 


12.01 


6.49105100 274.94 






12.01 


12.87 


0.86 


105148 274.08 




2.1012.87 


10.77 




105190,276.18 


(Foot of bank, which 


2.1810.77 


8.59 




105200 278.36 


-j rises perpendicu- 












( larly 1 foot. 


7.19 


8.59 


1.40 




105300 285.55 




3.80 


8.22 


4.42 




105400 289.35 




1.45 


4.42 


2 97 




105500 290.80 





ON LEVELLING. 



63 







FIELD NOTES- 


-Working Section. 


Rise. 


Back 
sight. 


Fore 
sight. 


Fall. 


Distance. 


Reduced 
Levels. 


Remarks. 












290.80 


Brought forward. 




2.97 


3.39 


0.42 


105600 


290.38 






3.39 


5.51 


2.12 


105700 


288.26 






5.51 


7.67 


2.16 


105800 


286.10 






541 


6.68 


1.27 


105827 


284.83 


Edge of ditch. 




6.68 


8.56 


1.88 


105832 


282.95 


Bottom of ditch. 


2.48 


8.56 


6.08 


6.30 


105837 


285.43 


Top of bank. 




6.08 


12.38 


4.34 


105854 


279.13 


Foot of bank. 




12.38 


16.72 


0.62 




274.79 






2.04 


2.66 


3.82 


105900 


274.17 






2.66 


6.48 


2.38 


105940 


270.35 


Edge of ditch. 




6.48 


8.86 




105944 


267.97 


Bottom of ditch. 


2.86 


8.86 


6.00 


1.58 


105952 


270.83 


Top of bank. 




6.00 


7.58 


3.16 


105960 


269.25 


Foot of bank. 




7.58 


10.74 


4.91 


106000 


266.09 






3.33 


8.24 


0.91 


106095 


261.18 


Top of bank. 




8.24 


9.15 


4.19 


106100 260.27 


Stump, side of bank. 




9.15 


13.34 




106105 


256.08 


Bottom of ditch. 


1.69 


13.34 


11.65 


1.15 


106110 


257.77 


Edge of ditch. 




11.65 


12.80 


0.51 


106200 


256.62 






3.62 


4.13 




106300 


256.11 




0.75 


4.13 


3.38 




106349 


256.86 


Foot of bank. 


2.88 


3.38 


0.50 


3.85 


106359 


259.74 


Top of bank. 




0.50 


4.35 




106368 


255.89 


Bottom of side drain. 


0.27 


4.35 


4.08 


0.23 


106386 


256.16 


Centre of parish road. 




4.08 


4.31 




106405 


255.93 


Foot of bank. 


3.74 


4.31 


0.57 


2.45 


106415 


259.67 


Top of bank. 




0.57 


3.02 


0.41 




257.22 






0.99 


1.40 


1.43 


106430 


256.81 


Foot of bank. 




1.40 


2.83 


1.58 


106500 


255.38 






2.83 


4.41 


0.07 


106600 


253.80 






4.41 


4.48 




106700 


253.73 




0.46 


7.80 


7.34 




106800 


554.19 


C (Crosses foot-path at 
I 106831). 


2.93 


7.34 


4.41 




106900 


257.12 




3.67 


4.41 


0.74 




107000 


260.79 




4.20 


10.63 


6 43 




107100 


264.99 




5.06 


6.43 


1.37 




107200 


270.05 




5.79 


10.76 


4.97 




107300 


275.84 




3.85 


4.97 


1.12 


0.05 


107400 


279.69 




• 


5.42 


5.47 




107500 


279.64 




0.91 


5.47 


4.56 


0.44 


107600 


280.55 






4.56 


5.00 


0.56 


107637 


280.11 


Edge of ditch. 




5.00 


5.56 




107640 


279.55 


Bottom of ditch. 



64 



A TREATISE 



FIELD NOTES— Working Section. 



Rise. 


Back 
sight. 


Fore 
sight. 


Fall. Distance. 

1 


Reduced 
Levels. 


Remarks. 






1 


279.55 


Brought forward. 


3.16 5 56 


2.40 


0.56107647 


282.71 


Top of bank. 


1 2.40 


2.96 




107654 282.15 


Foot of bank. 


1.58 2.96 1.38 




1077001283.73 




8.84 9.45 0.61 




107800:292.57 




5.11 8.44 3.33 




107853,297.68 


Enter plantation. 


2.91 3.33 0.42 


1.50K 


B. M. on timber stub. 


12.7814.28 




107882299.09 




4.2714.2810 01 




107900303.36 




8.7510.01 1.26 




107947i312.ll 




10.4214.49 4.07 


108000322 53 




1.21 4.07 2.86 


0.491080081323.74 




1 2.86 3.35 




108024323.25 




2.98 3.35 


0.37 




108047 326.23 




i 

15.3316.35 

1 


1.02 




108098 341.56 


j Top of bank, edge ol 
[ plantation. 


1 1.02 


1.32 


0.30108100 341.26 




2.74 8.66 


5.92 


il08200.344 . 00 




0.78 5.92 


5.14 


1108300344.78 






5.14 


8.43 


3.29108400 341.49 






1.05 4.50 


3.45108500 338.04 






4.50 4.94 


0.44108520 337.60 






4.94 6.83 


1.89108530 335.71 


Edge of bank. 




6.8312.54 


5.71108540 330.00 


Foot of bank. 




12.5416.82 


4.28108600 325.72 






1.11 


9.04 


7.93108700:317.79 






1.18 


9.09 


7.91108800 309.88 






1.57 


9.70 


8.13108900 301.75 






1.28 


9.58 


8-30109000,293.45 






1.44 


9.41 


7.97109100 285.48 






1.34 


9.14 


7.80109200 277.68 






1.15 


8.12 


6.97109300 270.71 






3.04 


4.43 


1.39109386269.32 


Edge of ditch. 




4.43 


6.22 


1.79109390 267.53 


Bottom of ditch. 


1.06 


6.22 5.16 
5.1611.10 


■109400,268.59 Stump, top of bank. 
5.94109405 262 65 Foot of bank. 


1.8111.10; 9.29 


109500:264.46 


3.10 


8.87 


5.77 


109600 267.56 At post and rail fence. 


1.17 


4.63 


3.46 


1109700,268. 73. Edge of slope. 




3.46 7.06 


3.60109800 265.13 




1.96 4.60 


2 . 64 109900 262 . 49, Foot of slope. 




4.60 4.60 


1110000 262. 49j 


0.93 


4.60 3.67 


1110149 


263.421 




4.58 5.03 


0.45110377 


262.97 Stump, end of curve. 


0.63 


5.03 


4.40 






263.60 On rails at end ol curve. 




4 40 


4.58 


0.18 




263.4*2 B. M. foot ol post. 


3.53 


4.58 1.05 






266.95 Top of said post. 



ON LEVELLING. 65 

In taking levels for a minute section where the 
observations must be very numerous, and consequently 
the back and fore sights not very far from each other, 
the observer will frequently be able to make a number 
of observations at each setting up of the level at one 
side of his line, so that his instrument may be about 
equally distant from his back and fore observations. 
Due attention to this will save much time and labor, 
and experience will enable the surveyor at a glance to 
see where he can setup his level at every remove forward 
with the greatest advantage. Upon looking down our 
field notes above, it will be seen it seldom occurred that 
only one back and one fore sight was obtained at a 
setting up of the level, and this only took place where 
the ground was very steep : by the first setting up of 
the instrument four forward sights were observed, and 
of course as many back ones ; thus the first back sight 
was 4.47, the corresponding fore sight 4.53 ; this latter 
number was also placed as the back sight for the next 
observation, which was 9.22 ; this number was in like 
manner placed as the back sight for the next forward 
observation, 5.07, which also became the back sight for 
the last forward observation we could obtain at that 
setting up of the instrument, namely, 0.24 : it should 
here be remarked that there was a necessity to place 
each forward reading as a back observation to the next 
forward reading, otherwise the difference of level be- 
tween each point of observation would not have been 
obtained without more arithmetical work ; the numbers 



66 A TREATISE 

otherwise only show the difference of level between each 
and the first point of observation ; besides, by this ar- 
rangement, the whole section is continuous, however 
numerous the intermediate observations may be, and 
having the distances opposite, the whole can be plotted 
off with facility. The columns of Rise and Fall need 
no observation after what has already been said upon 
this subject. The column of distances denotes the con- 
tinuous measurements from the commencement, Gun- 
ter's chain being the unit employed. Our notes com- 
mence at the 1033rd chain, and terminate with the end 
of the work, 1103 chains and 77 links, which we con- 
sider an ample extract for the purposes of the student. 
The column headed " Reduced Levels " contains the 
height of each point of observation above the datum 
line, which in this case was Trinity high- water mark, 
London Bridge : these numbers are obtained by adding 
the " rises " and subtracting the " falls " from the pre- 
ceeding reduced level, which in our notes commence 
with 270.72 feet. 



THE SECTION. — SEE PLATE III. 

The datum line must be drawn, every chain should 
then be pricked off and the perpendiculars erected ; the 
chains or stakes should then be numbered beneath the 
datum line, to prevent mistake, and just above the 
datum line the height of the surface at each stake should 
also be inserted ; then the said heights can be pricked 



ON LEVELLING. , 67 

off upon the perpendiculars respectively, and the inter- 
mediate heights plotted from the field notes without fear 
of error, which otherwise, without great care, would 
be likely to occur in consequence of so many points 
falling near to each other, unless the scale be very 
large : the horizontal scale of the example is 1 inch to 
5 chains, and the vertical scale 1 inch to 25 feet. Hav- 
ing drawn the undulating line of the surface through 
these points upon the perpendiculars, the gradients or 
intended line of railway may next be laid down ; the 
extreme left-hand point was given, being the level of 
the rails at the point of junction with another line. 
The railway is represented by two parallel lines, the 
upper one being the upper surface of the rails, and the 
lower one the bottom of the ballasting or formation level 
being 2.25 lower than the surface of the rails ; for a 
short distance the line is level, then it rises at the rate 
of 20 feet per mile, for the two-fold object of dimin- 
ishing the great cutting and of getting sufficiently high 
over the road at stake 1064, to allow (with the low- 
ering the surface of the said road a small quantity) of 
sufficient headway for the public carriages to pass under 
the railway ; from this point the line falls at the rate 
of 20 feet per mile for a considerable distance, the ob- 
ject being to get as low down as possible further to the 
eastward, where there was to be a considerable embank- 
ment, and by these means such embankment was re- 
duced in dimensions ; and furthermore, the earth from 
the cutting to the right of the road was to be taken east- 



68 A TREATISE 

ward to form the said embankment, and therefore the 
down-hill gradient was favourable for carrying on the 
work as well as for the drainage of the cutting. Part 
of the earth from the large cutting was also to be taken 
to the eastward ; the ascending gradient, up to the 
bridge, was unfavourable for this purpose, however, so 
far as the bringing out the bottom of the cutting, the 
upper part being brought down by means of inclined 
planes ; the ascending gradient was unavoidable in this 
case, but by judiciously working the excavation, little 
inconvenience and extra expense attended it. Each 
change of gradients is denoted by a strong vertical line 
from the datum to the point of change, and the height 
marked thereon. The quantity of earth-work to form 
the cuttings and embankments with different slopes 
should be written upon them, as shown in our example ; 
also over the line of figures denoting the height of the 
surface above the datum should be placed the depth of 
the cutting from the surface to formation level at the 
same point, or the height of the embankment, as the 
case may be ; these heights and depths are those from 
which the calculations of the quantities are to be made, 
and therefore must be strictly correct ; they should not 
be taken from the section by the scale, but should be 
obtained by calculation ; the former method being liable 
to error. The calculation may be thus performed. 
Let it be required to find the depth of cutting at stake 
No. 1083, where the height of the surface above datum 
is 344.78 feet ; at stake No. 1064, the height of forma- 



ON LEVELLING. 69 

tion level above datum is 269.20, from which point the 
gradient descends at the rate of 20 feet per mile, or 
0.25 feet per chain, towards No. 1083 ; the distance 
from 1064 to 1083 is 19 chains, which multiplied by 
0.25, gives 4.75 for the fall of the railway in the inter- 
val between the two points ; consequently the height 
of the railway above datum at No. 10.83 is 269.20, 
minus 4.75 = 264.45 ; this sum, subtracted from the 
whole height of the surface, gives 344.78 — 264.45 === 
80.33, for the depth of the cutting at that point, and 
so of all the remaining numbers. After giving the 
above particulars nothing need be added upon this sub- 
ject. It may be worth observing, that in laying down 
the gradients care should be had so to dispose them as 
to produce the minimum quantity of work in the exe- 
cution, and that the cuttings should equalize the em- 
bankments, or, if anything otherwise, they should be 
a little in excess, to allow for subsidence or slips in the 
embankments. The facilities for working the excava- 
tions and carrying the earth to bank should also be 
considered ; a down-hill gradient in that direction is 
most suitable, provided it can be obtained without in- 
terfering with other and often more important consider- 
ations ; the drainage of the works during the formation 
and after the line is completed should also be consider- 
ed at the time of determining the gradients. We have 
inserted (Table I. at the end of the work) a very ex- 
tensive and useful Table of Gradients, which is suffici- 
ently self-explanatory as not to require further notice. 

5 



70 



A TREATISE 



When a surveyor is required to level through a coun- 
try in a perfectly straight line, and has not the advan- 
tage of its being picketed or poled out, his only means 
to keep a rectilineal course is by ascertaining, as ac- 
curately as possible, the magnetic bearing of one ex- 
tremity from the other, and work in that direction by 
means of a compass. We once had business of this 
kind, and determined the bearing of our intended line 
from the map of the Ordnance survey (allowing for the 
variation of the needle), and after pursuing the route 
thus determined, we were surprised and delighted at 
finding how exactly we came to our required point, con- 
vincing us (if a proof had been required) how justly 
the public confidence has been placed in our national 
survey. 

It is seldom the case in practice that the instrument 
can be placed precisely equi-distant from the back and 
forward staves, on account of the inequalities of the 
ground, &c. It would appear, therefore, to be neces- 
sary, to make our results perfectly correct, to apply to 
each observation the correction for curvature and re- 
fraction, as explained in the early pages of our book ; 
this, however, we believe, is seldom done unless in par- 
ticular cases, where the utmost possible accuracy is 
necessary, on account of the smallness of such correc- 
tion, as may be seen by referring to our Table, page 
13, where the correction for eleven chains is shown to 
amount to no more than T -J- ¥ of a foot ; and as the 
difference in the distances of the instrument from the 



ON LEVELLING. 71 

back and fore staves can in no case equal that sum, it 
is evident that such correction may be safely disregard- 
ed in practice. 

Several machines have been constructed or designed 
for the purpose of describing a section of any ground 
passed over by the instrument, which at the same time 
would register the distance passed over, as well as the 
undulations : perhaps the best of this kind was the one 
designed and constructed by George Edwards, Esq., 
Civil Engineer, of LowestofF, which is fully described 
and illustrated in the forty-fourth volume of the 
"Transactions of the Society of Arts," page 123, to 
which we refer. The use of such machines, however, 
must, from the nature of the work to be performed, be 
of a very limited character. 

We have now described the leading principles and 
practice of levelling as employed in engineering opera- 
tions ; and although our observations may appear to 
be confined to its applicability to railroad purposes, 
yet the intelligent student will find no difficulty in ap- 
plying to practice the same principles to every other 
branch of the profession where levelling operations 
may be required. We might indeed have multiplied 
instances and examples which would in reality have 
had no other effect than to swell our volume, as it must 
have been, to a great extent, but simply a repetition 
of the details already given. 

Before closing this subject we cannot refrain from 
stating, that it has long been our opinion that if a 



72 A TREATISE 

register could be kept by some public body (as the In- 
stitution of Civil Engineers) of the height of particular 
spots throughout the kingdom, above some given 
datum, as Trinity high-water mark, London Bridge, or 
any other that might be agreed upon, such a record 
would be invaluable both in a particular and national 
point of view ; to the engineer and geologist it would 
be most important, and the whole register could be 
prepared from time to time at a trifling cost, if each 
engineer and surveyor would but contribute to the com- 
mon stock by sending to head-quarters the level of any 
particular spots as he, in the course of his professional 
engagements, may have opportunity of determining 
them. We consider that no time is likely to be so 
favourable for the purpose as the present, as nearly the 
whole country has been levelled over for railway pur- 
poses within the last few years ; and no doubt the 
field notes of the greater part are still in existence 
from which a great many such standard levels could be 
extracted by the parties who took the levels, and which 
in a few years it will be impossible to eliminate. By 
way of showing more fully our meaning, we have ex- 
tracted from our own levelling books a few such stand- 
ard levels, and arranged them after the manner we 
have above alluded to. 



ON LEVELLING. 



73 



COUNTY OF KENT. 
Height in feet above Trinity high-water mark, London Bridge, 

Upper edge of tablet over door of No. 1 Martello Tower, 

near Folkstone 256.4 

Top of first milestone on the road from Folkstone turnpike 

to Dover 402.9 

Top of second milestone, do 510.7 

Surface of ground at Folkstone turnpike gate 534.6 

Dock wall at Dover, opposite Railway Office 7.4 

COUNTY OF SURREY. 

Surface of ground at New Chapel Turnpike gate 188.0 

Waste board of Godstone Ponds, back of White Hart Iun 319.2 
Top of twentieth milestone (from Westminster Bridge) 

on the road from Godstone to East Grinstead 287.6 

River Medway (tributary stream) meadows, west side of 

turnpike road, at Blundley Heath 151.2 

Broadham Green, near Oxted, foot of pointing post 268.2 

COUNTY OF SUSSEX. 

Honey-pot Lane, South Chailley Common... 122.5 

Gullage Farm, source of the Medway, near the barn 324.6 

Waste weir canal (east side of Lindfield) 82.1 

Summit of South Downs at Plumpton Plains 682.5 

at Mount Harry 573.3 

Turnpike road, Brighton to Lewes, near the barracks ... 85 1 

Cross roads, at Turner's Hill turnpike gate 535.2 

LEVELLING WITH THE THEODOLITE. 

The application of the theodolite to the practice of 

levelling is an operation of great simplicity. We must 



74 



A TREATISE 



suppose the reader to be already acquainted with the 
construction and method of measuring angles with that 
valuable instrument ; and those who have no such 
knowledge, we refer to the Treatise on Mathematical 
Drawing Instruments spoken of, where every particu- 
lar respecting it may be found. The ordinary 5 -inch 
theodolite, of the best construction, is the one we re- 
commend to the use of the surveyor, it being sufficient- 
ly accurate for most purposes that fall within his pro- 
vince, and is convenient to use on account of its porta- 
bility. A larger theodolite is seldom employed, except 
on surveys of great extent upon trigonometrical prin- 
ciples, as those of the United Kingdom under the di- 
rection of the Board of Ordnance, where theodolites of 
3 feet diameter have been employed to obtain the re- 
quisite degree of accuracy. 

To use the theodolite in the common purposes of 
levelling, it is only necessary to set the instrument up 
at every spot on the line of country to be levelled, 
where the inclination changes, without regard to the 
minor inequalities of the surface, taking care that the 
adjustments have been carefully examined and recti- 
fied, as explained in the book above alluded to, espe- 
cially those adjustments which set the line of collima- 
tion, and the spirit-level attached to the telescope, par- 
allel to each other. Then set the instrument level by 
means of the parallel plate screws, and direct an assis- 
tant to go forward with a staff, having a vane, or cross 
piece, fixed to it exactly at the same height from the 



ON LEVELLING. 



75 



ground as the centre of the axis of the telescope. 
Having gone to the forward station, the assistant must 
hold the staff upright, whilst the observer measures the 
vertical angle, which an imaginary line connecting the 
instrument and staff makes with the horizon ; the in- 
strument and staff should then change places, or, to 
save time, another staff should take the place of the in- 
strument, and the instrument be removed to the for- 
mer staff, and from thence the same angle should be 
taken back again, and the mean taken as the correct 
result. 

The distance must then be measured, which will fur- 
nish all the data required to find the difference of level 
between the places of the instrument and staff; this, it 
will appear evident, is a matter of trigonometrical cal- 
culation,* the measured distance being considered as 
the hypothenuse of a right-angled triangle, of which 
the perpendicular is the difference of level. It scarce- 
ly appears necessary to give the rule for the calcula- 
tion, but for the sake of uniformity we shall do so.f 

Add together the logarithm of the measured distance, 
and the log. sine of the observed angle; the sum, rejecting 
10 from the index, will he the log. of the difference of lev- 
el, in feet or links, &c, the same as the distance was 
measured in. 

If the distance be measured with G-unter s chain, the 
result (in chains) can at once be obtained in feet, by 

* Capt. Frome's Work, in 8vo, published 1840. 
t See Appendix I. 



76 A TREATISE 

simply adding to the above two logarithms the con- 
stant 1.8195439, which (10 being rejected from the in- 
dex) will give the log. of the height in feet. 

In this manner, by considering the surface of every 
principal undulation as the hypothenuse of a right- 
angled triangle, the operation of levelling may be car- 
ried on with great rapidity, but, it must be remarked, 
without pretensions to great accuracy ; in fact, in that 
particular, the use of the spirit-level will never be su- 
perseded. 

Another method of applying a theodolite to the pur- 
poses of levelling was introduced by Sir John Macneill. 
He caused to be constructed, by Messrs. Troughton and 
Simms, a more powerful instrument for the purpose. 
It was a combination of the level and the theodolite. 
He set it up at the foot of an inclination, and sent a 
man on with a staff, as above described ; and whilst 
the observer was looking through the telescope, anoth- 
er assistant walked along the line, holding up another 
staff at every rise and hollow of the intervening sur- 
face, and thereby the observer could note how much 
such rises and hollows were below the line of his vision* 

The distances from the instrument to the points 
where the staves were held up could then be measur- 
ed, and the section drawn by simply ruling a line at 
the angle of elevation given by the instrument (or, 
more correctly, by computing the total elevation, and 
setting that up as a perpendicular, and drawing the 
hypothenusal line thereto), and marking thereon the 



ON LEVELLING. 77 

measured distances, and from such marks drawing per- 
pendiculars of the various lengths indicated by the 
staff at its different positions : a line connecting the 
extremities of the perpendicular will represent the sec- 
tion of the surface line. 

Instead of measuring the distances, Sir John Mac- 
neill had attached to the eye-end of the telescope a 
beautifully made wire micrometer, similar to those ap- 
plied to astronomical telescopes, by which he could tell 
with sufficient accuracy the distances required. This 
method of levelling, like the former by the theodolite, 
will give but a general approximation to the truth, de- 
pending in a great degree upon the quality of the in- 
struments, and the care bestowed upon the operation. 



PART III. 

COMPUTATION OF EAKTH-WOKK— KOAD-MAKING— 
THE CLINOMETEE, ETC. 

We have now to show the manner of applying a sec- 
tion to practical purposes. If the object to be attain- 
ed is the making of a railroad, it is essential that it be 
formed as nearly level, and as perfectly straight, as the 
surface of the ground will admit of ; for the nearer it ap- 
proximates thereto, the more profitably will it be work- 
ed when completed, as locomotive steam-engines per- 
form the most work with the least expense when the 
resistance they have to overcome is uniform and in- 
variable. The same remarks hold with respect to a 
turnpike road ; but the inclinations on the latter may 
be made greater and more variable, being worked by 
animal power, which is capable of putting forth, on a 
sudden emergency, a greater exertion for a short time, 
which is not the case with elemental or mechanical 
power beyond limits much short of what an animal is 
capable of. 

Sir Henry Parnell, in his valuable Treatise on Roads, 
recommends that a road should not be made steeper 
than 1 in 35 ; that is, for every 35 feet in length of 
road surface, the difference of level will be 1 foot, that 
being an inclination which presents no difficulty to fast 
driving either in ascending or descending. But on a 



80 A TREATISE 

line of railroad to be traversed by locomotive engines, 
no rate of inclination, or gradient, as it is called,* 
should exceed 20 feet in a mile, or 1 in 264. To draw 
the lines of proposed surface (or gradients) upon a sec- 
tion, which shall be the most suitable for the purposes 
intended, and at the same time to be the most econo- 
mical in the execution, that is to say, to have the 
least possible quantity of earthwork in cuttings and 
embankments, requires judgment and experience ; no 
definite rules can be given for this purpose, as no two 
sections present the same undulating surface. There 
is one material point we would suggest, and which should 
be carefully attended to ; viz., that for every piece of 
cutting, there should be an equal, or rather less, quantity 
of embankment. We say rather less because every 
newly formed embankment experiences a settlement 
to a greater or less degree, and therefore more earth 
will be required to raise it to a proper level. The ex- 
cess of the cuttings above the embankments should 
never be great, otherwise the surplus would have to 
be disposed of in mounds, termed spoil-banks. In no 
case whatever should the required embankments exceed 
in cubical contents the quantity of cuttings ; for then 

* Sir John Macneill in his preface to his valuable translation of M. Navier's 
little work on the " Means of comparing the respective Advantages of differ- 
ent Lines of Railway," says, "I have rendered the word peute by slope 
in preference to inclination, inclined plane, or gradient, considering the two 
former, though generally used, as improper expressions ; and the latter, to 
say the least of it, as having so little to recommend it, that I hope it will 
have an extremely short existence in our nomenclature." 



ON LEVELLING. 81 

a serious difficulty occurs — land has to be purchased for 
the purpose of digging earth to supply the deficiency, 
which is usually called side cutting. 

Suppose inihe cut below the upper figure to represent 
the section of an old line of road, and that it were re- 
quired, by cutting and embankment, to reduce it from 
its present hilly surface to one uniform rate of inclina- 
tion from the point A to the point B. The lower 



Cross Sections. 



extremity A is 10 feet above the datum line of the 
section, and the higher point B 46 feet above the datum ; 
consequently, 46 — 10 = 36 feet, the rise from A to 
B, and the distance 4356 feet, which, divided by the 
rise (36), will give 1 in 121 for the rate of inclination 
the road may be brought to. 

Upon the section draw the straight line A B, which 
will show the extent of cutting and embanking to be 
made. The number of cubic yards of earth to be re- 
moved in the cutting between the points B and C, and 
the cubical contents, in yards, of embankment between 
C and A, may then be computed in the following man- 
ner : 

Divide the quantities of cuttings and embankments 
as shown upon the longitudinal section, into triangles 



82 A TREATISE 

and trapeziums, determined by the undulations of the 
surface lines, as shown in the above engraving, where, 
in the cuttings, a and c are triangles, b a trapezium ; 
and in the embankments d and/ are triangles, e a tra- 
pezium. The form of the excavation and embankment 
is shown by the transverse or cross sections. Let the 
width of the roadway (or base of the cutting, and top 
of the embankment) be 50 feet, including the footpath, 
&c, on each side ; the slope of the cutting to be 1 h to 
1, that is, lh horizontal to 1 perpendicular ; conse- 
quently, where the depth is 20 feet, the width of the 
slope at the surface will be 30 feet ; the slope of the 
embankment to be 2 to 1, that is, for 19 feet perpen- 
dicular, the base is to be 38 feet. With these data, the 
cubical quantities, as computed by the valuable Tables 
of Sir John Macneill,* are as follows : 

Excavation 81517 yards. 

Embankment 57081 " 



24436 surplus cutting. 

"We have an excess of 24436 cubic yards of excava- 
tion, which is a quantity far too great. In order, there- 
fore, to make the quantity of cutting and embankment 
more nearly balance each other, it would be necessary 
to continue the embankment beyond the point A, which 
would lengthen the inclination, as shown by the dotted 

* " Tables for calculating the cubic quantity of earthwork in the cuttings 
and embankments of canals, railways, and turnpike roads." By Sir John 
Macneill, Civil Engineer, F.R.A.S., &c. 



ON LEVELLING. 83 

Hue drawn from the point B to a ; this dotted line 
would now represent the proposed surface of the road. 
By such means we diminish the quantity of cutting, 
and, at the same time, increase that of the embank- 
ments ; and also by lengthening the inclination, we 
reduce its steepness. The alteration of the proposed 
surface line must be so made, that the cubical quan- 
tities of excavation and embankment are nearly equal ; 
leaving, however, a preponderance in favour of the 
latter of about 10 per cent, to supply the deficiency 
occasioned by the consolidation and shrinking of the 
earth ; and if any portion of the excess be then re- 
maining, it may be disposed of in flattening the slopes 
of the embankments, when no more convenient mode 
presents itself. 

The quantities of earthwork on a given section de- 
pend upon the arrangement and disposition of the 
gradients, or proposed surface lines ; and there is no 
practical consideration of more consequence to the 
engineer, in laying out a proposed line of surface upon 
a section, especially if it be of any great extent (as the 
present projected lines of railway), than the most judi- 
cious distribution of the cuttings and embankments, 
which should not only be nearly equal to each other in 
quantity, but the .circumstances must be considered 
under which the various embankments have to be sup- 
plied, it not being alone sufficient that for every hol- 
low on the section there should be a corresponding 
protuberance, but that such protuberances be advanta- 



84 A TREATISE 

geously situated for filling the hollows ; for otherwise 
the work assumes a character of difficulty, in conse- 
quence of the great additional expense of removing the 
earth to a considerable distance ; and if, in addition, 
the material has to be conveyed up an ascent, it will 
be more tedious in the execution. 

Knowing the value of practical examples in ele- 
mentary books, we shall here give the calculations of 
the above results in full, both by the common method ; 
viz., The Prismoidal Formula, and Sir John MacneilFs 
Tables, by which the saving of labour by the use of 
the Tables will be made apparent. 

Prismoidal Formula. — The area of each end added 
to four times the middle area, and the sum multiplied 
by the length divided by 6, will give the solid content. 
If the measures used in the calculation are yards, the 
result will be the content in cubic yards ; but if they 
are feet, the result must be divided by 27, to obtain 
the corresponding number of yards. 

CALCULATION OF THE TRIANGULAR PORTION a. 

Height 0. 
2) 18 

Height. . 18 9 mean height. 

Slope 1.5 1.5 slope. 



9.0 45 

18 9 



27.0 13.5 

Base 50 50<0 ( base (bottom of cutting, 

( or top oi embankment). 

77 63.5 



ON LEVELLING. 



85 



Brought forward, 77 

Height 18 



Area of 
greater end 



616 

77 

1386 



63.5 

9 mean height. 



571.5 middle area. 
4 



2286.0 4 times middle area. 
1386.0 area of greater end. 



3672 
561 



9) 11444 



length. 



3672 
22032 
18360 

6) 2059992 

3) 343332 cub. content in feet 



12716 cub. content in yards. 



COMPUTATION OF 6. 

Height 18. Area, as before, 1386. 



20 height. 
1.5 slope. 


18) 
20 J 


heights. 


10.0 


2) 38 




20 


— 




— : 


19 


mean height. 


30.0 


1.5 


slope. 


50 base. 


9.5 




80 


19 




20 height. 









28.5 




goo f area between 
\ b and c. 


50 


base. 



78.5 



86 

Brought forward, 



A TREATISE 



78.5 

19 mean height. 



7065 

785 

1491.5 
4 



middle area. 



5966.0 4 times middle area. 
1386 area of lesser end. 
1600 area of greater end. 



8952 
858 



9) 426712 



length. 



71616 
44760 
71616 

6) 7680816 

3) 1280136 cub. content in feet. 



47412 cub. content in yards. 



COMPUTATION OP C. 

Area 1600, as before. 
20 



\ > heights. 



2) 20 



10 mean height. 
1.5 slope. 

50 



ON LEVELLING. 



87 



Brought forward, 50 

10 



15.0 

50 base. 

65 

10 mean height 

650 middle area. 
4 

2600 4 times middle area. 
1600 area of greater end. 

4200 
825 length. 

21000 
8400 
33600 

6) 3465000 

3) 577500 cub. content in feet. 

9) 192500 

21389 cub. content in yards. 



a = cub. content 12716 

b = cub. content 47412 

c = cub. content 21389 

Total cuttings 81517 cub. yards. 



88 


A TREATISE 




COMPUTATION OP 


EMBANKMENT d. 


19 height. 
2 slope. 


i ] 


heights. 


38 


2)19 




50 base. 


— 




— 


9.5 


mean height. 


88 


2 


slope. 


19 height. 


19.0 




792 


50 


base. 


88 









69 




1672 area 


9.5 

34.5 
621 


mean height. 




655.5 


middle area. 




4 





2622.0 4 times middle area. 

1672 area of greater end. 

4294 

820 length. 



85880 
34352 

6) 3521080 

3) 586847 cont. in cub. feet. 



9) 195616 



21735 cont. in cubic yards. 





ON LEVELLING. 




COMPUTATION 


op e. 


Height 


8. Area, as 


before, 1672 


8 height. 
2 slope. 


i] 


heights. 


16 


2)27 




50 base. 







— 


13.5 


mean height. 


66 


2 


slope. 


8 height. 


27.0 




528 area. 


50 


base. 



89 



77 
13.5 

385 
231 
77 

1039.5 
4 

4158.0 
1672 
528 

6358 

825 

31790 
12716 
50864 

6) 5245350 



mean height. 



middle area. 



4 times middle area, 
area of greater end. 
area of lesser end. 



length. 



3) 874225 cub. content in feet. 



9) 291408 



32379 cub. content in yards. 



90 





A TREATISE 




COMPUTATION OF /. 


Area, as before, 528. 


i\ 


heights. 


2)8 

4 
2 


mean height, 
slope. 


8 
50 


base. 


58 
4 

232 
4 


mean height, 
middle area. 


928 
528 


4 times middle area, 
area of greater end. 


1456 
330 


length. 


43680 
4368 




6) 480480 




3) 80080 


cub. content in feet 


9) 26693 




2966 


cub. content in yards. 



d = cub. content 21735 

e = cub. content 32379 

f = cub. content 2966 

Total embankment 57080 cubic yards. 



ON LEVELLING. 91 

The same quantities computed by Sir John MacneilVs 

Tables. 

THE CUTTINGS. 

COMPUTATION OF a. COMPUTATION OF &. 

Tabular No =22.67 Tabular No = 55.26 

Length 561 Length 858 



2267 44208 

13602 27630 

11335 44208 



Cont. of a in cub. yards =12717 Cont. of 6 in cub. yards = 47413.08 

COMPUTATION OF C. 

Tabular No = 25.92 

Length 825 



12960 
5184 
20736 



Cont. of c in cub. yards = 21384.00 

THE EMBANKMENTS. 



COMPUTATIC 

Tabular No . . . 


)N OF d. 

... =.3519 
50 


COMPUTATION OF C 

Tabular No = fiOOO 


Base 


Base 


50 






Tabular No... 
Length 

Cub. content. . 




Tabular No. . . 


17.5950 
. . + 8.914 


25.0000 
. . + 14.247 


Length , 


26.509 
820 


39.247 
825 




530180 
212072 


196235 
78494 
313976 


Cub. content.. 


= 21737.380 


= 32378.775 



92 A TREATISE 

COMPUTATION OF f. 

Tabular No = .1481 

Base 50 

7.4050 
Tabular No -f 1.580 

8-985 
Length 330 

269550 
26955 

Cub. content 2965.050 



KESULTS BY THE TABLES. 

CUTTINGS. EMBANKMENTS. 

a = 12717.9 d = 21737 .4 

6 = 47413.1 e= 32378.8 

c = 21384-0 / = 2965.0 



81515-0 57081.2 

By comparing these results with those obtained by 
the former process, it will be seen that the cubical 
quantity of cuttings differs but two yards, and that of 
the embankments but one yard. The computation by 
the Tables may be abbreviated by using but one place 
of decimals, which would be sufficiently accurate for 
practical purposes. Our object is to show the calcula- 
tions, by the Tables, in their greatest extent, which 
even then produce a great saving of labour, and, of 
course, a much greater probability of accuracy, in con- 
sequence of the fewer figures employed, than the for- 
mer process. 



ON LEVELLING. 93 

It will be seen that the calculation of the embank- 
ments by the Tables is a longer process than that of 
the cuttings, the latter being done by simply multiply- 
ing a number taken from the Tables (answering to the 
height or depth at each end) by the length ; whilst, for 
the embankments, the tabular number is first multi- 
plied by the base (or width of roadway), and to the 
product is added a second tabular number taken out 
at the same time as the first. The first series of Sir 
John Macneill's Tables contain the numbers corre- 
sponding to a base of 50, and a slope of 1 h to 1 (which 
is the slope of the cuttings in our example). But for 
a slope of 2 to 1, reference must be had to the second 
series of the same tables, which are applicable to every 
width of base, and from slopes varying from i to 1, to 
3 to 1. We have adopted this example to show the 
calculations both by the particular and general Tables, 
as the first and second series of the valuable work re- 
ferred to may be called. 

The following is an extract from Sir John Macneill's 
preface to his Tables : — " All practical engineers are 
well aware, by experience, of the inconveniences which 
arise from the length of time necessary for calculating 
the cubic quantity of earthwork in the cuttings and 
embankments of canals, railways, and turnpike roads* 
especially when the section is of considerable extent, 
and the ground very uneven. As calculations of this 
kind are frequently, on a short notice, required to be 
completed within a limited period, the consequence is, 



94 A TREATISE 

that errors are almost sure to be made, as a multipli- 
plicity of figures is necessary, though the calculations 
in themselves are so very simple. 

" To save time in making these calculations, and en- 
sure accuracy in the results, were the principal objects 
I had in view in constructing the following Tables ; how 
far I have succeeded, must be left to the decision of 
practical men, for whose use they were intended, and 
who are best able to judge of their utility. 

"An advantage may rise from the use of these 
Tables, which I had not at first contemplated. By the 
common but erroneous method of calculation, the 
cuttings may appear to be equal to the embankments ; 
yet when the work is carried into effect, a large quan- 
tity of earth may be required to make up the embank- 
ments, or there may be too much earth in the cuttings 
for the embankments, according to the shape or figure 
of the section, as will be shown hereafter. Such a cir- 
cumstance as this cannot take place if the following- 
Tables be used to ascertain the cubic quantities ; for, 
as they are calculated from the prism oidal formula, 
they will give the true cubic quantity in any cutting or 
embankment; and consequently, if the cuttings be laid 
down on the section to balance the embankments, they 
will be found in practice to do so, when the work comes 
to be executed. 

" Contractors very frequently find that they have 
more earth to move than they had previously calcula- 
ted upon from the section, and are, therefore, often 



ON LEVELLING. 95 

great losers. This, in most cases, arises from erroneous 
calculations ; for the common practice is, either to add 
the two extreme heights together, and to take half the 
sum for a mean height ; or to take half the sum of the 
areas at each end for a mean area. Both these methods 
are erroneous ; one makes the quantity too much — the 
other too little." 

SLOPES, ETC. 

As connected with the subject of earth-work, we 
may insert in this place some particulars respecting 
the arrangement of slopes in cuttings and embankments. 
They are usually expressed in terms of the height or 
depth of cutting, as half to one, one to one, two to one, 
&c, signifying that for every foot perpendicular, the 
cutting shall batter half a foot, one foot, two feet, &c. 

The slope adopted must depend upon the nature of 
the material worked upon. Solid rock may be left 
perpendicular, whilst loose friable material, or sand, 
will stand but a very small angle with the horizon. 
The true criterion to judge of the proper slope to work 
to, is to observe, if convenient, what slope or angle 
the materials naturally assume when left to themselves. 
To determine this by measurement would be trouble- 
some and tedious ; but by the aid of a small instru- 
ment called a clinometer, the angle which any sloping 
surface makes with the horizon may be at once meas- 
ured, and the ratio of the slope to the perpendicular, 
as one to one, &c, be readily deduced. As this very 



96 



A TREATISE 



useful portable instrument is not generally known, we 
shall subjoin an engraving and description of it. 

The following figure represents a clinometer, or, as 
it is called in some parts of the country, a batter level. 
It consists of a quadrant A B, of about two inches 
radius, attached to a flat bar C D, six inches long. The 
quadrant is graduated to degrees, from B towards A, 
and adjoining the divisions maybe inserted, if required, 




the corresponding ratio of the slopes, one to one, &c. 
An index bar, E, turns upon the centre of the quadrant, 
and carries a spirit-level by which the index may be set 
truly horizontal by the hand ; and whatever angle is 
there denoted on the quadrant, will be that of the slope 
required. At F is a hinge-joint, by which the bar C D 
may be folded up, and the instrument can then be de- 



ON LEVELLING. 97 

posited in a box of very small dimensions, and carried 
in the pocket without inconvenience. 

To use this instrument, open the hinge-joint, and rest 
the edge of the bar CD on the face of the slope to be 
measured ; then gently move the index E round its 
centre until the attached spirit-bubble assumes a cen- 
tral position in its glass tube, and the angle, indicated 
by the index on the graduated arc, will at once measure 
the inclination. The ratio of the slope to the perpen- 
dicular is represented by the natural co -tangent of the 
angle thus measured ; but as the observer may not have 
at hand a Table of natural co-tangents, &c, we have x 
annexed a Table at once showing the slopes correspond- 
ing to the various angles of inclination likely to be re- 
quired. 

It will appear evident, that the longer the bar C D 
is, the more accurate will the measure of the slope be ; 
but there is no necessity for the instrument to be en- 
cumbered with a long bar, which would destroy its 
portability, because it can easily be attached, by tying, 
to the end of a long straight rod, which can be fur- 
nished by any neighbouring carpenter, and the real 
slope of an undulating inclined surface can then be 
accurately measured. 



98 



A TREATISE 













Table of 


' Slopes 












Slope or 
Batter 
to 1 foot 
perpen- 
dicular. 


Ratio of 
Slope to 
perpendi- 
cular. 


Angle of slope. 


Slope or 
Batter 
to 1 foot 
perpen- 
dicular. 


Ratio of 
Slope to 
perpendi- 
cular. 


Angle of Slope. 


With 
vertical. 


With 
horizon. 


With 
vertical. 


With 
horizon. 


ft. in. 




o 


, 


o / 


ft. in. 




o 


, 


O / 


4 


4 1 * to 1 


1 


12 


88 48 


1 


1 to 1 


45 





45 


h 


A " i 


2 


23 


87 37 


1 3 


14 ■ 


* 1 


51 


20 


38 40 


I 


A " i 


3 


35 


86 25 


1 6 


14 « 


« 1 


56 


19 


33 41 


1 


-h " i 


4 


46 


85 14 


1 9 


11 ' 


' 1 


60 


15 


29 45 


14 


-fo-nearlyl 


5 


57 


84 3 


2 


2 ' 


' 1 


63 


26 


26 34 


Ik 


B to 1 


7 


8 


82 52 


2 3 


24 ' 


' 1 


66 


2 


23 58 


1| 


\ n early 1 


8 


18 


81 42 


2 6 


24 ' 


1 1 


68 


12 


21 48 


2 


£ to 1 


9 


28 


80 32 


2 9 


2| < 


< 1 


70 


1 


19 59 


2i 


i nearlyl 


11 


46 


78 14 


3 


3 ' 


■ 1 


71 


34 


18 26 


3 


4 to 1 


14 


2 


75 58 


3 6 


n ■ 


1 1 


74 


3 


15 57 


34 


.I. « 

i 4 


4 1 


16 


16 


73 44 


4 


4 « 


« 1 


75 


58 


14 2 


4 


i ' 


« 1 


18 


26 


71 34 


4 6 


H ■ 


4 1 


77 


28 


12 32 


44 


A ' 


« 1 


20 


34 


69 26 


5 


5 ' 


< 1 


78 


41 


11 19 


5 


1 2 


4 1 


22 


37 


67 23 


5 6 


54 ■ 


« 1 


79 


42 


10 18 


54 


A ' 


4 1 


24 


37 


65 23 


6 


6 « 


1 1 


bO 


32 


9 28 


6 


k « 


' 1 


26 


34 


63 26 


7 


7 ' 


■ 1 


81 


52 


8 8 


7 


ft ' 


4 1 


30 


15 


59 45 


8 


8 « 


* 1 


82 


53 


7 7 


8 


! ' 


■ 1 


33 


41 


56 19 


9 


9 * 


1 1 


83 


39 


6 21 


9 


1 ' 


1 1 


36 


52 


53 8 


10 


10 ' 


* 1 


84 


17 


5 43 


10 


« ' 


1 1 


39 


48 


50 12 


11 


11 ' 


1 1 


84 


48 


5 12 


11 


12 


4 1 


42 


31 


47 29 


12 


12 * 


< 1 


85 


14 


4 46 



It is very important, in fixing upon the slopes for 
the sides of an excavation or embankment, to approx- 
imate very nearly to the inclination at which the 
ground would naturally stand without slipping ; for if 
they be made greater than necessary, a large quantity 
of labour, and of the surface of the ground, will be 
uselessly devoted. The proper slope for each particu- 
lar soil can only be determined by observation and 
experience. " An embankment that would stand per- 
fectly firm, and bear the action of the weather, when 
formed of sand, gravel, or the debris of rocks, and 
other materials that do not retain water in their fis- 



ON LEVELLING. 99 

sures, would not last one winter, if it chiefly consisted 
of clay. The same remark applies with equal force to 
cutting, where it is made through a stratum of clay."* 
A slope of 1 to 1, that is, a slope of 45°, is found suf- 
ficient for ordinary earth ; for clay 1$ to 1, or a slope 
of 33° 41' with the horizon, may often be required, 
unless it can be mixed with open materials to prevent 
water collecting in the fissures produced by its shrink- 
age in dry weather. In other cases, so steep a face 
may be left as I to 1, or even i to 1 ; and the slope 
that will be likely to stand may easily be judged of, by 
knowing the nature of the strata which will be cut 
through, and examining its state when exposed in the 
surrounding district." 

At Boughton Hill, near Canterbury, there is a large 
cutting through London clay, which, together with the 
embankment at the foot of the hill, formed of the same 
material, has been constantly giving way. The slopes 
of the embankment have been flattened from time to 
time, and now assume some appearance of consolida- 
tion ; but the slopes of the cutting near the summit of 
the hill continue to slip down upon the roadway. 
From some cross-sections we were able to take a short 
time since, it appears that the original slope of the cut- 
tings was about 2 to 1, forming an angle with the ho- 
rizon of 26° 34' ; but the natural slope assumed by 
the soft clay where it has slipped is about 9°, or a lit- 
tle more than 6i to 1. 

* Tredgold on Kailroads, first edition, page 117. 



100 A TREATISE 



ON SELECTING A LINE OF COUNTRY FOR A ROAD OR 
RAILWAY. 

The choice of a suitable line of country for the for- 
mation of a turnpike-road, a railroad, or a canal, pre- 
paratory to the levels being taken, requires both 
judgment and care ; otherwise a fruitless expenditure 
of time in taking a number of trial-sections may be the 
result, if attended with no more serious and permanent 
inconvenience. A person undertaking such a work 
should previously devote a little time to obtain a 
knowledge of the country, its localities, its structure, 
and geological character : such knowledge will lead to 
the choice of several lines of direction, which appear 
to the eye as equally favourable ; it then becomes 
necessary to make such preliminary surveys as will en- 
able the engineer to adopt the one which, under all 
circumstances, is likely to prove the most advanta- 
geous. 

At p. 113 (1st edition) of the late Mr. Tredgold's 
work upon Railroads, we find the following observa- 
tions upon this subject: "In order to facilitate the 
choice of a line as it regards the surface of the country, 
the engineer may be reminded, that even in the dis- 
posal which nature has made of hills and valleys there 
is much system. Those things which to the first 
glance of the better-informed, and at all times to the 
ignorant, appear to be without order or arrangement, 
are the result of the uniform action of natural causes, 



ON LEVELLING. 101 

and are, in reality, capable of being traced and de- 
scribed with less difficulty than would be expected. 
Where a considerable tract of country is to be sur- 
veyed, the best index to its elevations and depressions 
is its streams and rivers ; these indicate every change 
of inclination, and, to the experienced eye, with con- 
siderable precision. It will also be observed, that each 
river has its system of valleys ; and except in a few 
instances, where the draining is effected by the 
outburst of an open stratum, a district, whose bound- 
ing ridge is easily traced, is drained by its river and 
system of valleys. 

" Having formed a tolerable idea of the best direc- 
tion for the road, the next step must be to make a more 
particular survey, with a view to fix nearly the precise 
line. We would recommend the principal engineer to 
have this done by rectangular lines, as infinitely superior 
to surveying by triangles, in giving him an exact knowl- 
edge of the surface of the country. Perhaps, with the 
assistance of a diagram, we shall be able to render the 
advantage of this method obvious. 

" Let A B be a portion of the intended line, and 
D the breadth of the country to be included in the sur- 
vey. At any suitable distances choose stations, a, a, a, 
their distances apart depending on the changes of level, 
and let the principal line A B, and also the cross lines 
bb,bb, &c, be accurately levelled, and then drawn, as 
shown in the figure, on the plan of the line of road. If 
the distance b b is required to be considerable, perhaps 

7 



102 



A TREATISE 



an additional line in the principal direction may be 
necessary. The etched lines show the form of the sur- 
face at the lines A B, b 5, b b, &c, on the plan ; and 




the latter being sections at right angles to A B, there 
is no difficulty in seeing the extent of cutting, or of 
embankment, that may be avoided by varying the 
position of the principal line. In fact, a plan of this 
kind, to a person familiar with sections, is better than 
a model of the country." 

The most advantageous direction for a line, either of 
roadway or railroad, intended to connect two places, 
is evidently that of a right line, both horizontally and 
vertically : if one extremity of the line is more eleva- 
ted than another, the straight line connecting them 
will be an inclined plane, having one uniform rate of 
inclination ; but if a uniform slope cannot be obtained 
in the direct line, it is necessary .to deviate therefrom 
to obtain, as nearly as the circumstances of the country 
will admit, such an inclined plane, or at least to obtain 
continued progressive rises, avoiding as much as pos- 



ON LEVELLING. 103 

sible the introduction of useless ascents, that is, ascend- 
ing where we must descend again, and vice versa. 
When a line of road is encumbered with numerous and 
extensive useless ascents, the wasteful expenditure of 
power in the conveyance of goods is very great, as the 
number of feet actually ascended is increased many 
times more than is necessary, if each height, when once 
gained, were not lost again. 

Sir Henry Parnell, in his valuable treatise on Roads, 
gives the following instances of this kind of road- 
making : — ' ' As one instance, amongst others, of the 
serious injury which the public sustain by this system 
of roadmaking, the road between London and Barnet 
may be mentioned, on which the total number of per- 
pendicular feet that a horse must now ascend is up- 
wards of 1300, although Barnet is only 500 feet higher 
than London ; and in going from Barnet to London, a 
horse must ascend 800 feet, although London is 500 
feet lower than Barnet." 

Another instance of this defect in road-engineering 
is observable in the line of the old road across the isl- 
and of Anglesea, on which a horse was obliged to as- 
cend and descend 1283 perpendicular feet more than 
was found necessary by Mr. Telford, when he laid out 
the present new line, as shown by the annexed Table : 



104 



A TREATISE 





Height of 

summit above 

high water. 


Total rise 
and fall. 


Length* 


Miles. Yards. 


Old road . . . 
New road. . . 


339 
193 


3540 
2257 


24 428 
21 1596 


Difference . . 


146 


1283 


2 592 



In choosing the best direction for a line of roadway, 
the rate of inclination which can be obtained, with a 
moderate outlay in cuttings and embankments, is a 
consideration of greater importance than the mere 
maintaining of a direct line. For though the measur- 
ed length of a circuitous route may be considerably 
greater than the length of a direct line, yet if the in- 
clinations in the former case are much more favorable 
than those in the latter, it must be evident that more 
may be gained in speed, with the same expenditure of 
power, than is lost by the increase of distance. Thus, 
if two roads rise, one at the rate of 1 in 15, and the 
other at the rate of 1 in 35, the same expenditure of 
power will move a weight through 15 feet of the one 
and 35 feet of the other, at the same rate. 

Upon the subject of the maintenance of turnpike 
roads, we shall annex an abstract of the General Rules 
for Constructing and Repairing Roads, laid down by 
the late Mr. Telford, and which is so fully treated upon 
in the important work of Sir H. Parnell on Roads. 



ON LEVELLING. 105 



SHAPE, OR TRANSVERSE SECTION. 

The roadway should be 30 feet broad ; the centre 
should be 6 inches higher than the level of the sides, 
where the junction of the surface, with the sloping 
edge of the foothpaths, or other defining bounds of the 
roadway, form the side channels ; at 4 feet from the 
centre (on each side) the surface should be half an inch 
lower ; at 9 feet, it should be two inches lower ; and at 
1 5 feet, its extreme edge, it should be 6 inches lower ; 
this will give the form of a flat ellipse, which is well 
adapted for carrying off the water to the side channels, 
without making the cross section of the road too round, 
and allow the sun and wind to have a greater effect in 
evaporation, and keeping the road dry. In giving the 
surface one uniform curvature from side to side, the 
surveyor should use such a level as is described at 
page 111. 

The footpaths should be 6 feet broad, and have an 
inclined surface of 1 inch in a yard towards the road ; 
its surface should not be lower than the level of the 
centre of the road, and the edge should be sloped down 
(and covered with green sod) to meet the roadway, and 
form the side channel to carry off the water from the 
surface. 

DRAINAGE. 

All open main drains should be cut on the field side 
of the road fences, and should lead to the natural wat- 



106 A TREATISE 

ercourses of the country ; in general they should be 
3 feet deep below the bed of the road, 1 foot wide at 
bottom, and from 3 to 4 feet wide at top. Stone drains 
and culverts should also be made under the road, and 
continued to the open side drains, or ditches ; side 
channels (before named) must be made on the road 
side, with openings of masonry into the cross drains, 
to prevent any water lying on the road, it being neces- 
sary, in order to preserve the surface of a road perfect, 
that it be kept completely dry. All land springs ought 
to be carried from the site of the road by under-drain- 
ing. 

FENCES. 

" All road fences should be kept as low as possible, 
never being allowed to exceed 5 feet in height, in or- 
der that they may not intercept the sun and wind, and 
diminish their effects in producing evaporation ;" and 
for the same reason no trees should be allowed to grow 
by the side of a road ; for by keeping the roads wet, 
they occasion the rapid wear of the materials of which 
they are formed. 

ROAD MATERIALS. 

The hardest description of stone should always be 
preferred, such as basalt, granite, quartz, &c. " The 
whinstones found in different parts of the United King- 
dom, Guernsey granite, Mountsorrel and Hartshill 
stone of Leicestershire, and the pebbles of Shropshire, 



ON LEVELLING. 107 

Staffordshire, and Warwickshire, are among the best 
of the stones now commonly in use. The schistus rocks, 
being of a slaty and argillaceous structure, will make 
smooth roads, but they are rapidly destroyed when wet 
by the pressure of the wheels, and occasion great ex- 
pense in scraping, and the constantly laying on of 
new coatings. Limestone is defective in the same re- 
spect. Sandstone is generally much too weak for the 
surface of a road ; it will never make a hard one. The 
hardest flints are nearly as good as the best limestone ; 
but the softer kinds are quickly crushed by the wheels 
of carriages, and make heavy and dirty roads. Gravel 
when it consists of pebbles of the harder sorts of stones 
will make a good road ; but when it consists of lime- 
stone, sandstone, flint, and other weak stones, it will 
not ; for it wears so rapidly, that the crust of a road 
made with it always consists of a large portion of the 
earthy matter to which it is reduced, and prevents the 
gravel from becoming consolidated, and the road from 
attaining that perfect hardness it ought to possess."* 
"When the materials are stone, they should be broken 
to a size of a cubical form not exceeding 2 2 inches in 
their largest dimensions, and should be capable of pass- 
ing through a ring of that diameter. When it consists 
of gravel, the pebbles which are from 1 to ltz inch in 
size only should be used for the middle part of the 
road ; all larger pebbles should be broken ; the small- 

* Abridged from Sir H. Parnellon Roads, page 271. 



3 08 A TREATISE 

er stones may be used for the sides of the roads and 
the foothpaths. 

THE FOUNDATION AND DISPOSITION OF MATERIALS. 

Before the foundation is laid, the surface on which it 
is to rest must be prepared, by making it level from 
side to side, and, if necessary, raising it so that the fin- 
ished surface of the road may not be below the level 
of the adjoining fields. If the subsoil be wet and elastic, 
it must be rendered non-elastic by whatever means is 
best adapted to overcome the cause, as drainage, &c. 
The foundation should consist of a rough close-set 
pavement, of any kind of stones that can be most 
readily procured ; those set in the middle of the road 
should be 7 inches in depth ; at 9 feet from the centre, 
5 inches j at 12 feet from the centre, 4 inches ; and at 
15 feet, 3 inches. They should be set with their broad- 
est faces downwards, and lengthwise across the road ; 
and no stone should be more than 5 inches broad on its 
face. " The irregularities of the upper part of the 
pavement should be broken off with the hammer, and 
all the interstices should be filled with stone chips, 
firmly wedged, or packed by hand with a light ham- 
mer ; so that, when the pavement is finished, there 
may be a convexity of 4 inches in the breadth of 15 
feet from the centre. 

" The middle 18 feet of pavement should be coated 
with hard broken stones, of the form and size describ- 
ed under the head 'Road Materials/ to the depth of 



ON LEVELLING. 



109 



6 inches. Four of these 6 inches to be first put on, and 
worked in by carriages and horses ; care being taken 
to rake in the ruts until the surface be- 
comes firm and consolidated, after which 
the remaining 2 inches are to be put on. 

" The paved spaces on each side of the 
18 middle feet should be coated with broken 
stones, or well-cleansed strong gravel, up to 
the footpath, or other boundary of the road, 
so as to make the whole convexity of the 
road 6 inches from the centre to the sides 
of it ; and the whole of the materials should 
be covered with a binding of an inch and a 
half in depth of good gravel, free from clay 
or earth." 

The footpaths should be made with a 
coating of strong gravel, or small broken 
stones, at least 6 inches deep. The annexed 
engraving exhibits a section of a road con- 
structed according to the above rules. 

REPAIRING ROADS. 

Towards the latter end of the autumn of 
each year, a road should be put into a 
complete state of repair, to preserve it 
from being broken up during the folio w- 
iDg winter, between which time and the preceding 
spring, all repairs, by laying on of new materials, 
should be done. If thin coatings be laid on at a time, 



110 A TEEATISE 

and when the ground is wet, they will soon be worked 
into the surface without being crushed into powder. 

All ruts and hollows should be filled up as soon as 
they appear. The side channels and drains should be 
continually kept clean, and free from obstruction ; and 
all damage they may have sustained be made good as 
soon as discovered. 

" A road should be scraped from time to time, so as 
never to have half an inch of mud on it ; the mud 
should not be scraped into, or allowed to remain in, 
the side channels, so as to stop the running of water 
in them. 

" The hedges should be kept constantly clipped and 
cut as low as possible, without rendering them unfit 
for confining cattle ; and all projecting branches of the 
trees in the fences should be lopped." 

In the minutes of evidence given before a Select 
Committee of the House of Commons on the subject of 
Steam Carriages, we find the following paragraph as 
part of the evidence given by Sir John Macneill : 

" Well-made roads, formed of clean, hard, broken 
stone, placed on a solid foundation, are very little af- 
fected by changes of atmosphere ; weak roads, or those 
that are imperfectly formed of gravel, flint, or round 
pebbles, without a bottoming or foundation of stone 
pavement or concrete, are, on the contrary, much 
affected by changes of the weather. In the formation 
of such roads, and before they become bound or firm, 
a considerable portion of the subsoil mixes with the 



ON LEVELLING. 



Ill 



stone or gravel, in consequence of the necessity of 
putting the gravel on in thin layers : this mixture of 
earth or clay, in dry warm seasons, expands by the 
heat, and makes the road loose and open ; the conse- 
quence is, that the stones are thrown out, and many 
of them are crushed and ground into dust, producing 
considerable wear and diminution of the materials : in 
wet weather, also, the clay or earth, mixed with the 
stones, absorbs moisture, becomes soft, and allows the 
stones to move and rub against each other when acted 
upon by the feet of horses or wheels of carriages. 
This attrition of the stones against each other wears 
them out surprisingly fast, and produces large quanti- 
ties of mud, which tend to keep the road damp, and 
by that means increase the injury." 




s\ 



Footpath. 



The above engraving represents the level employed 
by road-surveyors in laying out new works. On the 
horizontal bar A C are placed four sliding gauges, 
a, b, c, d, which move in dovetailed grooves cut in the 
horizontal bar, and when adjusted to their proper 



112 A TREATISE 

depth below the bottom edge of the level, can be firmly 
fixed in their position by a thumb-screw. A section 
of this portion of the instrument, taken through the 
line at e, is given on the right, drawn to a larger 
scale ; the remaining parts of the instrument require 
no explanation. 

For laying out slopes, the clinometer, described at 
page 96, is the best instrument that can be used. 



ON LEVELLING. 



113 



Table I. — -Showing the reduction upon each chain necessary to reduce 
hypothenusal to horizontal measure. 



Angle of 


Reduction 


Angle of 


Reduction 


Angle of 


Reduction 


ascent or 


in 


ascent or 


in 


ascent or 


in 


t de scent. 


liDks. 


descent. 


links. 


descent. 


links. 


O 1 

4 


£ 


O / 

23 48 


8* 


O / 

33 55 


17 


5 44 


* 


24 30 


9 


34 25 


17* 


7 2 


1 


25 11 


9* 


34 55 


18 


8 7 


1 


25 51 


10 


35 25 


18} 


11 28 


2 


26 30 


10* 


35 54 


19 


12 50 


2* 


27 8 


11 


36 24 


19* 


14 5 


3 


27 45 


lit 


36 53 


20 


15 13 


3* 


28 22 


12 


37 21 


20* 


16 15 


4 


28 58 


121 


37 49 


21 


17 15 


4* 


29 33 


13 


38 17 


21* 


18 12 


5 


30 8 


18* 


38 45 


22 


19 6 


51 


30 41 


14 


39 12 


22* 


19 57 


6 


31 15 


14* 


39 39 


23 


20 47 


6* 


31 48 


15 


40 6 


23* 


21 34 


7 


32 20 


15* 


40 33 


24 


22 20 


7* 


32 52 


16 


40 58 


24} 


23 5 


8 


33 24 


16* 


41 25 


25 



114 



A TREATISE 



Table II. — Gradients or Inclined Planes. 



Ascent or 






Ascent or 






Descent. 


Rate of 


Angle of 


Descent. 


Rate of 


Angle of 






inclination. 


inclination. 




inclination. 


inclination. 


Inl 


Inl 






Inl 


Inl 






mi.e. 


chain. 






mile. 


chain. 






feet. 


ft. dec. 




o f // 


feet. 


ft. dec. 




o / // 


1 


0.013 


] in 5280.0 


39 


51 


0.638 


1 in 103.5 


33 12 


2 


0.025 


.. 2640.0 


1 18 


52 


0.650 


.. 101.5 


33 51 


3 


0.038 


.. 1760.0 


1 57 


53 


0.663 


.. 99.6 


34 30 


4 


0.050 


.. 1320.0 


2 36 


54 


0.675 


.. 97.8 


35 10 


5 


0.0(53 


.. 1056.0 


3 16 


55 


0.688 


.. 96.0 


9 35 49 


6 


0.075 


. . 880 


3 55 


56 


0.700 


.. 94.3 


36 28 


7 


0.0S8 


.. 754.3 


4 34 


57 


0.713 


.. 92.6 


37 7 


8 


0.100 


..' 660.0 


5 13 


58 


0.725 


.. 91.0 


37 46 


9 


0.113 


.. 586.7 


5 52 


59 


0.738 


.. 89.5 


38 25 


10 


0.125 


.. 528.0 


6 31 


60 


0.750 


.. 88.0 


39 4 


11 


0.138 


.. 480.0 


7 10 


61 


0.763 


.. 86.6 


39 43 


12 


0.150 


.. 440.0 


7 49 


62 


0.775 


.. 85.2 


40 22 


13 


0.163 


.. 406.1 


8 28 


63 


0.788 


.. 83.8 


41 1 


14 


0.175 


.. 377.1 


9 7 


64 


0.800 


.. 82.5 


41 40 


15 


0.188 


.. 352.0 


9 46 


65 


0.813 


.. 81.2 


42 19 


16 


0.200 


.. 330.0 


10 25 


66 


0.825 


.. 80.0 


42 58 


17 


0.213 


.. 310.6 


11 4 


67 


0.838 


.. 78.8 


43 37 


18 


0.225 


.. 293.3 


11 43 


68 


0.850 


.. 77.6 


44 16 


19 


0.238 


.. 277.9 


12 22 


69 


863 


.. 76.5 


44 55 


20 


0.250 


.. 264.0 


13 1 


70 


0.875 


.. 75.4 


45 34 


21 


0.263 


.. 251.4 


13 40 


75 


0.938 


.. 70.4 


48 50 


22 


0.275 


.. 240.0 


11 20 


80 


1.000 


.. 66.0 


52 5 


23 


0.288 


.. 229.6 


14 59 


85 


1.063 


.. 62.1 


55 20 


24 


0.300 


.. 220.0 


15 38 


90 


1.126 


.. 58.7 


58 36 


25 


0.313 


.. 211.2 


16 17 


95 


1.188 


55.6 


1 1 51 


26 


325 


. . 203 . 1 


16 56 


100 


1.250 


.. 52.8 


15 6 


27 


338 


.. 195.6 


17 35 


110 


1.375 


48.0 


1 11 37 


28 


0.350 


.. 188.6 


18 14 


120 


1.500 


44.0 


1 18 7 


29 


0.363 


.. 182.1 


18 53 


130 


1.625 


.. 40.6 


1 24 38 


30 


0.375 


.. 176.0 


19 32 


140 


1.750 


.. 37.7 


1 31 8 


31 


0.388 


.. 170.3 


20 11 


150 


1.875 


.. 35.2 


1 37 38 


32 


0.400 


.. 165.0 


20 50 


160 


2.000 


.. 33.0 


1 44 8 


33 


0.413 


.. 160.0 


21 29 


170 


2.125 


.. 31.1 


1 50 39 


34 


425 


.. 155.3 


22 8 


180 


2.250 


.. 29.3 


1 57 9 


35 


0.438 


.. 150.9 


22 47 


190 


2.375 


.. 27.8 


2 3 39 


36 


0.450 


.. 146.7 


23 26 


200 


2.500 


.. 26.4 


2 10 9 


37 


0.463 


.. 142.7 


24 5 


220 


2.750 


.. 24.0 


2 23 9 


38 


0.475 


.. 138.9 


24 44 


240 


3.000 


.. 22.0 


2 36 9 


39 


0.488 


.. 135.4 


25 23 


260 


3.250 


; 20.3 


2 49 9 


40 


0.500 


.. 132.0 


26 3 


280 


3.500 


.. 18.9 


3 2 8 


41 


0.513 


.. 128.8 


26 42 


300 


3.750 


.. 17.6 


3 15 7 


42 


0.525 


.. 125.7 


27 21 


320 


4.000 


.. 16.5 


3 28 6 


43 


0.538 


.. 122.8 


28 


340 


4.250 


.. 15.3 


3 41 4 


44 


0.550 


.. 120.0 


28 39 


360 


4.500 


.. 14.7 


3 54 2 


45 


0.563 


.. 117.3 


29 18 


380 


4.750 


.. 13.9 


4 6 59 


46 


0.575 


.. 114.8 


29 57 


400 


5.000 


.. 13.2 


4 19 56 


47 


0.588 


.. 112.3 


30 36 


425 


5.313 


.. 12.4 


4 36 7 


48 


0.600 


.. 110.0 


31 15 


450 


5.625 


.. 11.7 


4 52 17 


49 


0.613 


.. 107.8 


31 54 


475 


5.938 


.. 11.1 


5 8 26 


50 


9.625 


.. 105.6 


32 33 


500 


6.250 


.. 10.6 


5 24 35 



APPENDIX 



In the former edition of this work there was an er- 
ror in the Rule which appears, in the present edition, 
at page 75, the word "tangent" having been written 
for "sine." A scientific friend, in noticing this mis- 
take, has suggested a convenient method of arranging 
the figures of the calculation when the perpendicular 
and base of a right-angled triangle are both to be com- 
puted from the base-angle and hypothenuse. The di- 
rections are as follows : — 

"1st. Write down the log. of the measured hypo- 
thenuse taken from the table of numbers. 

" 2nd. Over it place the log. sine of the measured 
angle from table of log. sines, &c, and draw a line 
above. 

11 3d. Under the log. of the hypothenuse write down 
the cosine of the angle, and then draw a line under it. 
Add the hypothenuse to the sine upwards, and it will 
give the length of the perpendicular sought in the table 
of numbers. Add the hypothenuse and cosine toge- 
ther downwards, and it will give the length of the base 
in the table of numbers. 



116 A TREATISE 

"Note. — I reject 10 from the log. index in both 
sums, beeause radius 10 stood in the first term, as a 
divisor, in both proportions. 



" EXAMPLE. 




"From A to C, I found the angle to be 6° rising— and the length 

of the hypothenuse A C measured 1240 links. 
" I state the calculation thus : 

2.112657 = log 129-& the perp r . 



2nd, Sine of 6° * = 9.019235 

1st, Hypothenuse 1240 = 3.093422 
3rd, Cosine of 6° = 9.997614 



3.091036 = log 1233^ the base. 
Answer: 

Perpendicular . . 129 T 6 (j- links. 

Base 1233 T 2 F do. 

Hypothenuse . . 1240 do. 

We may add here, in reference to the precept in 
italics, at page 75, that the constant number 1.8195439 
is the logarithm of 66, the number of feet in a chain. 



ON SETTING OUT THE WIDTHS OF GROUND REQUIRED 

FOR THE WORKS OF A 

RAILWAY OK CANAL, 

ETC., ETC., 

DEPENDING UPON THE DEPTH OF CUTTING OR 

HEIGHT OF EMBANKMENT, 

AND THE TRANSVERSE SLOPE OF THE NATURAL SURFACE. 



BY 
FREDERICK WALTER SIMMS, F.G.S., M.I.C.E. 

8 



" V 






ON SETTING OUT THE WIDTHS OF GROUND REQUIRED 



FOR THE WORKS OF A 



RAILWAY OR CANAL, 



When the natural surface of the ground, both longi- 
tudinally and transversely, is upon the same level as 
that of the intended works, the process of setting and 
staking out the widths is very simple. Let us take, 
for example, the case of a railway, the base or bottom 
width of which, when prepared for the reception of 
the ballasting and permanent way, is to be 36 feet ; 
the ratio of the inclination, or batter, of the slopes to 
the heights, both in the cuttings and the embankments, 
to be 2 to 1 ; beyond which, or at the outward edge, 
a slip of land 12 feet wide is to be taken on each side 
of the railway for the fences, &c. First, the centre 
line must be staked out and carefully levelled : it is 
customary to drive a stake, about 2 feet long and 
about U inch square, into the ground at each chain's 
length, their tops to be upon the fair level of the 
natural surface, thus affording good stations for the 
levelling staves to be held upon ; the relative level of 
each stake being then very accurately determined with 



120 A TREATISE 

respect to some given datum, they become so many 
zero points for reference in the subsequent operations. 
From each of the centre stakes a line must be set out 
on both sides, and at right angles to the centre line, 
or at right angles to a tangent to the centre line at 
that point, if the centre line be curved : upon these 
transverse lines the required widths of land must be 
set out. Now, if the ground at any of the centre 
stakes is upon the same level as the intended base of 
the railway, nothing more will be required than to 
measure on each transverse line, and in both directions 
from the centre stake, one half the required width, 
which, in our supposed case, is 18 feet for the half 
width of the railway, and 12 feet for the fences ; in all 
30 feet on each side of the centre. But when, as it 
mostly happens, the ground is not on the proposed 
level of the railway, the operation is not quite so sim- 
ple ; and if in addition thereto the ground slopes side- 
wise or at right angles to the general direction of the 
line, the business is still more complicated, and requires 
some skill and care to do the work correctly. The 
method of doing this it is now our business to explain. 
The next most simple case to the above is when the 
cross section of the ground is horizontal, be the depth 
of cutting or height of embankment what it may. 

Centre Stake. 



ON LEVELLING. 



121 



This is shown in the preceding diagram, which repre- 
sents a cross section of a 20 feet cutting, with slopes 
of two horizontal to one perpendicular. The horizontal 
line A B at right angles to the centre line represents 
the natural surface of the ground. Under these cir- 
cumstances it will readily be seen that the half width 
of the cutting, or the distance from 
the centre to the edge of the slopes 
C and D, equals the half width of 
the base (18) added to the batter 
of the sloping sides (40), and in- 
cluding the 12 feet for the fences, 
the total half width of land required 
for the purposes of such railway- 
would be 18 + 40 + 12 — 70 feet, 
and consequently the whole re- 
quired width to be appropriated 
and fenced in for a 20 feet cutting 
or embankment, when the ground 
does not slope sidewise, would be 
140 feet. 

The next and more complicated, 
and also the most frequently oc- 
curring case, is, when the cross 
section of the natural surface is not 
horizontal, as shown in the annexed 
diagram, which also represents a 
cutting of 20 feet. 

Let the line A B represent a horizontal line passing 



Centre* 




122 A TREATISE 

through the centre line C of the railway, which, if it 
coincided with the surface of the ground, would give 
A C and C B (each half width) 70 feet, as in the former 
example, the depth of cutting and the slopes being 
assumed the same. 

Let the line E H represent the natural surface of 
the ground upon this transverse section ; it will readily 
be perceived that the real half width C E (on the left 
of the diagram) is much shorter than the horizontal or 
computed half width A C, because the ground-line is 
depressed on that side of the centre ; likewise the half 
width C H on the other side of the centre is greater 
than the said horizontal or computed half width, be- 
cause the ground is there elevated above the horizontal 
line A B passing through the centre. To determine 
exactly the distances C E and C H in actual operations 
in the field, would be attended with some difficulty, 
and consume much time ; but the following method, 
at the same time that it gives a sufficiently correct 
approximation in practice, is also a very expeditious 
one : 

Let us suppose that the point E or distance C E be 
known, and that with a spirit-level we determine the 
difference of level between the points C and E, this 
difference is represented by the line E F, which sup- 
pose to be one foot ; now we have a small right-angled 
triangle A E F, of which E F is determined, being the 
difference of level (one foot), and the slope or ratio of 
A F to E F also given (2 to 1), therefore the side A F 



ON LEVELLING. 123 

is known (2 feet), which, subtracted from the computed 
half width A C, leaves F C approximately equal to E C, 
the required half width, sufficiently exact for all prac- 
tical purposes, where the cross section of the ground 
does not differ materially from a horizontal line. 

We have been supposing that the point E is known, 
whereas that point is the object of our search ; in 
practice, therefore, we proceed thus : — Take the com- 
puted half width, and if the ground is depressed, let a 
levelling staff be held somewhat nearer the point G 
than the said computed half width, for a first approx- 
imation to the point E ; then determine the difference 
of level between this assumed point and the centre 
point C, multiply this difference of level by the ratio of 
the slopes (which doubles it when the slope is 2 to 1), 
and subtract the result from the computed half width, 
which gives a more correct approximation to the point 
E ; now hold the staff at this new point and find the 
difference of level as before, again multiply by the ratio 
of the slopes, and deduct the result from the computed 
half width, which second result will in most cases be 
sufficiently near the real half width for a depressed line 
for all practical purposes. 

Example. — Central height (or depth of cutting), 20 
feet, slopes 2 to 1, base 36 feet ; the computed half 
width was therefore 58 feet ; the ground being depres- 
sed, we estimated that the point E might fall short of 
the computed half width 2 feet : we therefore directed 
a levelling staff to be held at 56 feet from the centre 



124 A TREATISE 

line (or stake) C, at which point another staff was held, 
and, by means of a spirit-level set up at a convenient 
distance, we found the difference of level between these 
points to be 0.87 foot, which, multiplied by the ratio of 
the slopes (2 to 1), gave 1.74 foot to be subtracted from 
the computed half width, 58 feet, leaving 56.26 feet for 
a first approximation to the half width C E (see last dia- 
gram). Now, upon removing the staff to this new 
point, the difference of level was again taken (or rather 
we should say that the staff was again read off, as the 
level had not been disturbed), and found to be 0.91 
foot, which also multiplied by the ratio of the slopes 
(2 to 1), gave 1.82 foot to be substracted from 58 feet, 
leaving 56.18 for the second approximation, and which 
was adopted as the correct half width for the depressed 
side of the centre ; indeed, in such a case as is above 
given, where the ground is so nearly horizontal, the 
first approximation (taken by a person after a little 
practice) may be assumed as the correct result, for in 
the above example it differed but .08 from the second 
determination, and if it had been taken a third time it 
could not have been more accurate as far as practice is 
concerned ; this, however, is not the case where the 
inclination or slope of the ground is considerable, for 
then (if this method be followed) several approxima- 
tions will be necessary to bring the result within ad- 
missible limits. 

When the ground is elevated above the horizontal 
line, as shown on the right hand of the diagram, the 



v 0N LEVELLING. 125 

mode of procedure will somewhat differ : thus, instead 
of holding the staff and finding the difference of level 
at a less distance than the computed half width, it must 
be held at a greater distance to obtain the point H by 
approximation ; the difference of level between that 
point and the centre point C being equal to H I, which 
multiplied by the ratio of the slopes, will give the dis- 
tance B I to be added to the computed half width C B, 
to obtain the half width CH; this may likewise be 
repeated to obtain a more correct result, as described 
for the other or depressed side of the centre C. It will 
also here be obvious to a person possessing but the 
smallest share of mathematical knowledge, that this 
result is not strictly correct, inasmuch as the line C H 
can never be equal to C I, but for practical purposes it 
is, as before observed, sufficiently correct. It may not 
be altogether unnecessary to observe, in this place, 
that the corrections B I, &c, as shown in the foregoing 
diagrams, are much exaggerated, being far greater in 
proportion to the computed half width C B, than ever 
occurs in ordinary practice, but this has been done to 
make our explanations more distinct than they other- 
wise would be. 

The above particulars have been confined to the case 
of excavations ; we must now show in what the pro- 
cess differs when the ground is to be covered with an 
embankment. 

By reversing page 120 we invert the diagram, which 
then represents an embankment. The rule for finding 



126 



A TREATISE 



the half width for an embankment where the transverse 
section of the ground is horizontal, remains the same 
as for the cuttings under like circumstances, as may- 
be seen by an inspection of the in- 
verted figure of the first diagram ; 
but upon inverting the second dia- 
gram, it will at once be seen that 
some variation in the process is re- 
quired. Thus : 

The horizontal line is represented 
by that marked A B ; C D and C F 
are the computed half widths ; C E 
the required half width on the de- 
pressed side, and C H the required 
half width on the elevated side, the 
line K L representing the natural 
surface of the ground. In the case 
of an excavation, we have shown 
that the real half width is greater 
on the elevated side than the com- 
puted half width, and less on the 
depressed side ; but it will be seen 
by the above diagram that for an 
embankment the real half width is 
less on the elevated side, and greater 
on the depressed side, than the com- 
puted half width ; therefore, in determining the ap- 
proximate place of the point E on the depressed side 
for an embankment, the staff must be held further from 




ON LEVELLING. 127 

the centre than the computed half width ; and for the 
point H, or the elevated side, it must be held nearer to 
the centre than the computed half width ; and finally, 
for computing the real half widths from the differences 
of level between the points E and the centre, and H 
and the centre ; on the depressed side the difference of 
level multiplied by the ratio of the slopes is to be added 
to the computed half widths to obtain the point E, and 
to be subtracted from the computed half widths to ob- 
tain the point H. 

The process above described may appear to the 
reader a very tedious one ; it perhaps is so to read ; 
but a little practice will convince him that it is a very 
expeditious method, for in most cases one setting up 
of the level will answer for several stations, and the 
multiplication by the ratio of the slopes upon such 
small numbers as mostly occur is easily performed, 
especially if it be an even number, as 2 to 1. The 
columns of the field-book may be arranged as in the 
following example for making the calculations in the 
field, or may be abridged to suit a more convenient- 
sized book for the pocket, at the pleasure of the sur- 
veyor ; indeed, all that can be accomplished now of 
this kind is to give general rules, which can be altered 
and arranged to suit the convenience of the surveyor, 
as experience may point out a more suitable mode of 
proceeding. The example is taken from an extensive 
field operation by the writer, and shows the work both 
for a cutting and an embankment ; the change from 



128 A TREATISE 

one to the other, or the tailing out of the cutting, as it 
is called, being included therein. The slope of the 
cutting is calculated at ltz to 1, and that of the em- 
bankment at 2 to 1. The width of the railway was 36 
feet, consequently half the said width was 18 feet. 



ON LEVELLING. 



129 



Eeqnired half 
width for edge of 
Cutting or foot of 

Embankment. 


d 




Feet. 
44.86 

20.97 


20.46 
21.52 
19.24 


CM 

CO 



CM 


CM 

CO 

06 

rH 


(M CO rH CM O 
O CO 00 CO O 

<m cri cm' ■hj os 

CM CM CO CO CO 


,3 

§ 

02 


Feet. 
58.74 

25.50 


27.94 
28.92 
25.80 


CM 
CM 


CO 

OS 
CM 
CM 


rH UO CM CO lO 
10 CO CO t- CO 

OS •*& CO CO rH 
rH CM CM CM CO 


Difference of Level, 
X ratio of Slope. 


6 

O 


Feet. 
- 7.08 

+ 0.11 


CO CO 

qcot> 

CO CM CM* 

1 1 1 


CO 
rH 

O. 
+ 


O 

CO 

1 


-* ^H b- CM CO 

(N©WHI> 
rH CM CO CO CO 

1 II 1 1 


1 1 1 1 r 


d 


02 


O t* O O GO O ^H 

.00 CO rtf CO t- CO rH 

■g CO tH "* ^' CO CO rH 

*+ + +++ + + 


b- t- <M "^H fc- 

<M CO CO OS CO 
rH CM CM C4 CO 

I 1 1 1 1 


Difference of Level. 

+ 


d 

O 




IO CO CO rH CO t— 

HHridrlri 

1 1 l + l 1 


CO CO IO CO CM 
OOt>(NO»3 

O rH CM CM CM 

1 1 1 1 1 


Feet. 
- 3.54 
J + 0.07 ' 
1 - 1.50 


n 1 1 1 r 


d 

O 
02 


O (M 

."<* CO 

■Sco cq 
*+ + 


O O 05 
(MtHQO 
CM CM rH 

1 I 1 


+ 1.90 
+ 0.57 


•ooooocio 

OO iO CO OS CM 

O rH rH rH CM 

1 1 1 1 1 


III 


Is 
13 

© be 

^ i 

n « 

O ■*» 

a> a 


O 

S5 


Feet. 
3.96 

3.24 


CO CM tH 

CMHI> 

"tf JO CO 


CO 
<M 




CM 


(M CM t- <M CO 

IOCN(MOI> 
O CO r* CO* CM 
rH 


<6 

"S 

CD 


Feet. 
7.50 

4.74 


O CM CO 
00 ^ rH 

»o" co 10 


O 
rH 


to 

CO 


IO CO CM O CO 
CO OS IO rH CM 
rH t^ CO »0 id 
rH 


d 


02 


Feet. 
10.90 

7.06 


O CM CM 

CO 
CO CO t^ 






CO 


CM 

JO 


O CO O CO CO 
CNIOtHOO 

oi o» ad i> i> 

rH 


j^eq pa^ndraoo 


Feet. 
51.94 

0.86 


23.54 
24 J 2 
22.02 


9 

O 
CM 


cm' 

CO 
rH 
CM 


CO CM ^ O CM 
t> O tJ; It- CM 

O t^ OS rH HO 

<M CM CM CO CO 


•^n9ni5[Ui3qTii 
Sat^no jo q 


U jo 


KMENT. 

Feet, 

16.97 

1.43 


287 2.77 

288 3.06 

289 2.01 


CM 
CM 
rH 

O 
OS 
CM 


rH 
OS 

rH 

rH 
OS 
CM 


OS rH CM »0 rH 
CO iO t- CO CO 

rA ri? O CO CO 

6 


•8WS J< 


) -ok 


EMBAN 
285 

286 


£j CM CO -Tfl IO CO 

c-\ os os os os os 

p CM CM CM CM (M 
O 



130 A TREATISE 

The first column contains the number of the central 
stakes, reckoned from the commencement of the work, 
which are convenient for reference. 

The second column contains the depth of cutting or 
the height of embankment, as the case may be, at that 
point on the centre line. 

The third column, the computed half width from the 
centre line to the edge of the cutting, or foot of em- 
bankment, upon the supposition that the ground is 
horizontal at right angles to the centre line ; this half 
width, as before explained (p. 121), is found by multi- 
plying the central height by the ratio of the slopes, 
and adding to the product half the width at the base of 
the railway. 

The fourth, fifth, and sixth columns contain the read- 
ings from the levelling staves at the centre stake, and 
at the approximate points E and H (see last diagram). 

The seventh and eighth columns contain the differ- 
ences of level between the centre stake and the above 
approximate points. These numbers are simply the 
differences of the quantities in the three preceding col- 
umns (except at stakes 286 and 290, which we will 
presently explain), and the signs ~|- and — denote 
whether they are positive or negative quantities, as 
respects the centre and the approximate points E and 
H. 

The ninth and tenth columns contain the differences 
of level (contained in columns 7 and 8) multiplied by 
the ratio of the slopes, and must have the same signs 



ON LEVELLING. 131 

-f or — as the corresponding numbers in the preceding 
columns. 

The last two columns contain the final half widths 
obtained by adding or substracting, according to the 
prefixed signs -f- or — , the numbers in the two pre- 
ceding columns to the computed half width contained 
in column 3. 

After the explanations already given, the reader can 
find no difficulty in tracing the steps of the example, 
except perhaps with the stakes 286 and 290, where the 
difference of level on the north side is represented by 
two numbers bracketed together, one having the sign 
+, and the other - : for the stake 286 the real differ- 
ence of level on the north side the centre is a rise of 
1.50, that is, the approximate point H is 1.50 foot 
above the centre stake : but it happens that the height 
of the embankment itself at that point is to be but 
1.43 foot (column 2) ; therefore the approximate point 
H is above the intended top of the embankment, and 
consequently will not represent the foot of an embank- 
ment, but the edge of a cutting, and therefore the cal- 
culation for the half width on the north side must be 
treated as for a cutting whose depth is equal to the 
height of the approximate point H above the intended top 
of the embankment ; or, in other words, the excess of 
the difference of level between the centre stake and the 
approximate point H, above the intended height of the 
embankment, is the quantity to be entered in the col- 
umn (7 or 8) " Difference of Level," and to be com- 



132 A TREATISE 

puted as for a cutting instead of embankment. In the 
case of stake 286 this excess is 0.07, to which is pre- 
fixed the sign plus ; this sum multiplied by the ratio 
of the slope being additive (for a cutting) on the ele- 
vated side of the centre, as before explained. 

For the stake 290, the north side of the line (column 
6) is 1.34 higher than the centre stake, and it, being 
embankment, would have the sign — prefixed (as 
shown by the lower number, column 8) : but the cen- 
tral height of the embankment at that point is but 1.22 
(column 2) ; therefore, 1.34 - 1.22 = 0.12, which is 
the depth of cutting on the elevated side, and when 
multiplied by the ratio of the slopes is to be added to 
the computed half width to obtain the correct result. 
When the surface of the ground is much inclined at 
right angles to the centre line, the numbers to be 
operated upon become proportionally large. 

As it is a case of frequent occurrence that one side 
will be a cutting when the other is an embankment, 
we wish it to be well understood, and therefore annex 
the accompanying diagram to illustrate it. 

The line F G represents the natural surface of the 
ground, A B the horizontal line at the centre stake, 
C D the intended height of the embankment, K L the 
width or base of the railway, 36 feet, part of which is 
an embankment and part a cutting ; the point E, or 
foot of the embankment, will be determined in the 
usual way, as explained at page 126 ; but the point 
H, which is to be the edge of the cutting, must be 



ON LEVELLING. 



133 



found by subtracting T> (the * 
height of embankment) from H I 
(the difference of level) ; the re- 
mainder, H M (which is the excess 
of the difference of level between the 
centre stake and the approximate 
point H above the intended height of 
embankment)^ multiplied into the 
ratio of the slope, must be added 
to the computed half width, or, 
in other words, treated as for a 
cutting, to obtain the said point 
H, as before stated. By revers- 
ing the diagram the correspond- 
ing case will become evident ; 
namely, when the centre line is 
in cutting, and one side on em- 
bankment, while the other is in 
excavation ; and the mode of pro- 
ceeding will at once strike the 
reader after perusing what we 
have above written. 




EXAMPLES OF THE MODES 



OF SETTING OUT 



RAILWAY CURVES. 



By HENRY LAW. 



EXAMPLES OF THE MODES 
OP 

SETTING OUT RAILWAY CURVES. 



-vert* 



There are very few lines of railway so favorably sit- 
uated as to be free from curves of greater or less ex- 
tent, and occurring more or less frequently in their 
course ; and consequently a knowledge of the method 
of correctly and readily laying down these curves upon 
the ground becomes a very necessary and important 
qualification in those engaged in setting out lines of 
Railway. It has not therefore been considered out of 
place to append to a work treating on one of the most 
important branches of railway surveying, a description 
of the various methods which may be employed for this 
purpose. 

Previously, however, to proceeding to the more 
practical part of the subject, it may be desirable to 
make a few observations upon railway curves in gen- 
eral. The curve which has been almost universally 
employed in laying down lines of railway, is the arc of 
a circle, although it may be shown that, under certain 



138 A TREATISE 

circumstances, this curve is not theoretically that which 
should be employed, as affording the least danger from 
the centrifugal tendency of the carriages. It has been 
generally considered that the true curve was one which 
commenced with an infinite radius, decreasing in a 
regular manner in advancing on the curve, until the 
minimum radius of curvature required had been at- 
tained. This form of curve has, however, been deduced 
upon the assumption that the whole of the centrifugal 
tendency of the carriages is balanced by the superele- 
vation of the outer rail, an assumption which is only 
correct on the supposition of the wheels of the car- 
riages being cylindrical, or no play being allowed be- 
tween the flanges and the rails — conditions which are 
never fulfilled in practice. For it may be shown, that 
with conical wheels, and a certain amount of play, a 
portion of the centrifugal tendency will always be coun- 
teracted by the self-acting adjustment produced by the 
lateral deviation of the carriage on the rails, however 
small the radius of curvature may be ; and that when 
the radius exceeds a certain limit, this adjustment 
is perfect, no superelevation of the outer rail being 
then required. 

It is obvious, therefore, that in curves whose radii 
are within this limit, the true form for the curve is one 
whose radius of curvature at its commencement should 
equal this limit, and should decrease in advancing upon 
the curve, according to such a law, that (assuming the 
rise in the outer rail to form a regular inclined plane) 



ON LEVELLING. 139 

the unbalanced centrifugal tendency should at every 
part of the curve be exactly counteracted by the amount 
of the superelevation of the rail at that part ; until the 
top of the incline being reached, the radius of curva- 
ture should then remain constant, being such that the 
centrifugal tendency of the train should be exactly bal- 
anced by the combined effect of the lateral deviation 
of the carriages on the rails, and the superelevation of 
the outer rail. When, however, the radius of curva- 
ture exceeds this limit, it may be shown that the arc 
of a circle is preferable to any other form of curve. 

Now, if we put d for the diameter of the wheels of 
the carriages, w for the width of the gauge of the line, 
and p for the lateral play allowed on each side, between 
the flanges of the wheels and the rails (all the dimen- 
sions being expressed in feet), and n being the ratio of 
inclination of the tire of the wheel ; then 

n d w 

—. — = Jtt I. 

will be the limit above referred to ; that is, R will be 
the least radius of curvature which may be used with- 
out the necessity of raising the outer rail. And for 
any other smaller radius, putting v for the velocity of 
the train in miles per hour, and r for the radius of the 
curve in feet ; then „ 

.782 v 2 (ndw — 4 p r) TT 

= -J-—1 = e . II. 

n a r 

will be the superelevation of the outer rail in inches, 



140 A TREATISE 

which will be required for that radius, in order that 
the whole of the centrifugal tendency of the train may 
be destroyed. 

Although we have thus shown that for all curves 
having a smaller radius than R, it would not be cor- 
rect, theoretically , to employ the arc of a circle, it is 
nevertheless very questionable whether it would be 
advisable, in practice (except under peculiar circum- 
stances), to substitute the theoretical curve in its stead, 
inasmuch as the circular arc possesses the practical ad- 
vantage of being laid down upon the ground with far 
greater facility ; and the only real objection which can 
be made to its use — namely, that of requiring a sud- 
den and instantaneous superelevation of the outer rail 
at the point where the curve commences — may in a 
great measure be removed by commencing to raise the 
rail before arriving at this point, and making the rise 
form a gradual inclined plane, whose summit shall be 
attained at the commencement of the curve. By the 
adoption of this plan, although the centrifugal ten- 
dency (as without it) commences suddenly, the counter- 
acting force produced by the superelevation of the outer 
rail, at the same instant attains its maximum, and the 
two forces therefore balance each other. Whereas, 
without it, the sudden commencement of the centrifu- 
gal force, being entirely unopposed, would at first 
tend to throw the carriages off the line, until, by the 
gradual elevation of the outer rail, it had been entirely 
destroyed. 



ON LEVELLING. 141 

Having thus far pursued the inquiry as to which 
form of curve it is most expedient to employ in prac- 
tice in laying down a line of railway, and having shown 
that with hardly an exception the arc of a circle is 
practically the best, we shall confine ourselves to de- 
scribing a few of the most generally applicable 
methods by which the circular arc may be traced on 
the ground. 

The first method which we shall describe is that 
which has in practice been perhaps the most ex- 
tensively used, although it possesses some objections, 
which we shall point out in the sequel. Let A B and 




C D be the two straight portions of the fine which it 
is desired to connect by a curve, B and C being the 
two points at which the curve falls into the straight 
lines ; and let B b lt b 1 b 2l b 2 5 3 , &c, be the distance 
which it is desired that the points to be found in 
curve shall be apart : then measure upon the straight 



142 



A TREATISE 



line A B produced, the distance B a 1 , equal S x in for- 
mula IY. below, and from the point a x set off, perpen- 
dicular to the same line, the distance a 1 b t1 equal to 
o x in formula III., which will give the first point 
required in the curve ; then range a straight line 
through the points B, b 1} and upon this line lay off 
the distance b 11 a 2 , equal to S 2 in formula YL, and 
from the point a 2 set off, perpendicular to the line 
Ba 2 , the distance a 2 b 2 , equal to o 2 , in formula Y., 
and the point b 2 will be the second point in the curve ; 
then in a similar manner range another line through 
the points b x b 2) upon which measure the distance 
b 2 a B , equal to the distance S 3 or 5 1 a 2l and from a s 
setoff as before, perpendicular to the line b ± a 3 , the 
distance a B b 3 , equal to o 2l which will determine the 
third point in the curve ; and thus proceed until the 
whole extent of the curve has been set out. 

In order to obtain the values of 8 lt S 2J o l5 and o 2 , let 
r equal the radius and d equal the distance B b lt or b x 
b 2 , &c, which it is desired that the points found in the 
curve shall be apart (both expressed in feet) ; then 

£- = <>! ni 

2 r L 

Vd*—o 1 * = d l IV. 



r 
<*(*— °i) = * VI. 



o 2 V. 

r 2 



r 
As an example of the application of this method, 
let the radius of the curve (r) be 15 chains or990 feet, 



ON LEVELLING. 143 

and the distance B b x (d) one chain or 66 feet; then 
from formula III.j 

66 2 
2X990 = 2 - 2feet==0 ^ 

will be the first offset at a x ; and 

V66 2 — 2.2 2 = 65.963 feet = ^ 

will be the distance B a 1} to be laid off upon the line 
A B produced to give the place for this offset. Again, 
66 X 65 .963 . QQ _, , 

will be the offset at a 2 , a s , a 4 , &c. ; and 

66 X (990 -2.2) aKQK . 

— ^\ Q0 = 65.85 feet = d 2 

will be the distance h 1 a 2 , b 2 a 3 , &c, to be measured 
from the points b t , b 2J &c, in order to give the points 
a 2 , a s , a±, &c, from which the offsets o 2 are to be 
taken. 

To this method there are, as has been already stated, 
some practical objections, inasmuch as any error which 
may be committed, in setting out only one of the 
points in the curve, will occasion a corresponding error 
in every succeeding one ; and a very trifling inaccu- 
racy in calculating either the distance S a , or the length 
of the offset o 2 , from its being frequently repeated, 
may ultimately cause a very considerable deviation 
from the true curve. Both these objections, however, 
may be in a great measure removed by the adoption 
of the following method of checking the position of 



144 A TREATISE 

about every fifth point ; or, which would be better, 
first determining the position of these points, and then 
filling in the intermediate ones ; and as we consider 
this modification does away almost entirely with the 
above-mentioned sources of error, we shall give an ex- 
ample of its application. 

Let us suppose r and d, or the radius, and the dis- 
tance the points B, b 1 , b 2 , &c, are apart, to be the 




same as in the last example — viz., 990 feet and 66 
feet respectively, and let it be determined to check 
the position of every fourth point : then the values of 
Sj, S 2 , o x , and o 2 , will be the same as before ; but 
previous to setting out the points 1, 2, 3, &c, we 
must calculate the distance B B t to be measured 
along the line A B produced, and the distance B 1 4 to 
be set off from the point B x to give the position of 
the fourth point in the curve, which may be done as 



ON LEVELLING. 145 

follows: Let the distance B B 1 equal A lt and B 2 4 

equal 1 ; and let D j be the length of the chord line 

connecting the two points B and 4 and /? be the angle 

a Bjj then 

o, rad . n 

and 

2 r sin 4 /? 



rad 



D x . 



Then, by substituting D 1? 1} and A lt for eZ, X and 
S lt in the formulae III., IV., Y., and VI., we shall 
obtain the values of 1} A ±1 2 , and A 2 where A 2 is 
the distance 4 B 2 to be measured upon the chord line 
B x 4 produced, and 2 is the distance B 2 8 to be set 
off from B 2 in order to give the eighth point in the 
curve ; for the values of r and d given above we shall 
obtain 

Logo x = 0.342423 = log 2.2 

Log rad = 10.000000 

10.342423 
Logc* = 1.819544 = log 66 



Log sin = 8.522879 

and p = 1° 54' 37" V 4 P = 7° 38' 28" ; then 

Log2r = 3.296665 = log 1980 

Log sin 4/3 = 9.123745 



12.420410 
Log rad = 10.000000 



LogD x = 2.420410 = log 263.27. 



146 A TREATISE 

Then from formula III. 

263.27 2 
2X990 =35feet;==O i ; 

from formula IV, 

-Z263.27 2 — 352 =260.92 feet = A, ; 

from formula V. 

263.27 X 260.92 



990 
and from formula VI. 



69.4 = 2 ; 



263.27 X (990- 35) __ 

990 ~ 25 ™ b ~ * 2 * 

These being obtained, the position of every fourth 
point should be first determined by the dimensions 
A .j, lt A 2 , and 2 ; and then the intermediate 
points 1, 2, 3, 5, 6, &c., by S 1 , o ly 5 2 , and o 2 , as first 
described. 

The second method which we shall describe may be 
advantageously employed when the radius of curvature 
is large and the centre can be seen from every part of 
the curve. 

Let the lines A B and CD as before represent the 
two straight portions of the line required to be con- 
nected by a curve having a radius of 80 chains or 1 
mile. First set up a theodolite at B and another at 
C (the two terminations of the straight portions of the 
line) and from each point range a line at right angles 
to the lines A B and C D respectively, and at the 



ON LEVELLING. 



147 



intersection of these lines (E), which will be the centre 
of the curve, put up a signal sufficiently conspicuous to 




be seen from any point between B and C. Then pro- 
duce the straight lines A B and C D until they intersect 
in the point F, and on these lines drive in stakes at 
equal distances, a 1 , a 2 , a 3 , &c, commencing from the 
points B and C. If r equal the radius, and § equal the 
distance between the points a l7 a 2l a 3 , &c, both in 
feet, then 

will be the distance which must be set off from the 



148 A TREATISE 

first point a li not perpendicular to the line B F, but 
in the direction a t E ; in like manner 

Vr 2 +2d[ 2 - r = o 2 

will be the distance to be set off from the point a 2 in 
the direction a 2 E ; and generally 

vVa-f-^Tdia - r = o n 

will be the distance to be set off at the nth points 
from B and C. 

For example, let r be 5280 feet and S equal 100 
feet: then 

•v/52802 + 100 2 — 5280 = .94 feet = o x 

will be the distance a 1 b 11 which must be set off from 
a 1 in the direction a x E to obtain the first point b 1 in 
the curve ; and proceeding in a similar manner with 
the others, the following Table will exhibit the dis- 
tances to be set off at the respective points a lt a 2 , a s , 
&c. : 



a x or 


100 feet from B, 


the offset will be 


.94 


a 2 


200 


<c 


a 


3.79 


a s 


300 


a 


n 


8.52 


a * 


400 


a 


tt 


15.13 


a s 


500 


a 


ti 


23.62 


a e 


600 


tt 


tt 


33.98 


a, 


700 


a 


tt 


46.19 


a s 


800 


a 


tt 


60-26 


a 9 


900 


a 


tt 


76.16 


«10 


1000 


a 


tt 


93.86 


a ix 


1100 


a 


tt 


113.36 



ON LEVELLING. 149 

At a 12 or 1200 feet from B, the offset will be 13465 
a,. 1300 « " 157.68 



14 



lT 



1400 
1500 



182.45 
208.93 



If the extent of the curve is such that the length of 
the offsets before reaching the point F, where the two 
tangent lines intersect, become inconveniently long, so 
as to occasion loss of time in setting them off, it will 
be advisable to make use of another tangent line as 
shown at G I ; for determining the position of which 




line the following method made be made use of. Let 
r, as before, be the radius, £ the number of degrees 
contained by the angle B E C, and n the number of 

10 



150 A TREATISE 

tangent lines (as B G, G H, H I, I C) intended to be 
employed ; then 



r sin 



= r tan — 
n 



cos 



will be equal to the length of any one of these tan. 
gent lines. As an example, let r be equal to 5280 feet, 
s equal to 60°, and n equal to 4, so that the quotient 
of s divided by n will be 15° : then the calculation for 
the length of each of the lines B G, G H, &c, will be 
as follows : — 

Logr =3.722634 

Log tan — = 9.428052 

3.150686 = log 1414 

Hence the length of each of the lines B G, G H, &c, 
will be 1414.8 feet, 

Now, having ascertained this length, nothing more 
remains than to set it off from B and C towards F, and 
then to range a line G I from the two points thus ob- 
tained, which will be the required tangent line : this 
line must then be bisected in the point H, which may 
readily be done by ranging a line from F to E, which 
having been done, proceed as already described to set 
off the equal distances a 1} a 2l a z , &c, from B and H 
towards G, and from H and C towards I ; and then by 
setting off the distances a lt b 1 , a 2 , h 2 , &c, contained 
in the table already given, from the several points a 11 
a 2 , &c, in directions radiating to the centre E, the 



ON LEVELLING. 151 

course of the curve will be marked by the points b lt 
b 2 , b 3 , &c, thus obtained. 

One advantage possessed by the above method is, 
that, knowing exactly the direction in which to lay off 
the offsets (and that by the range of a comparatively 
distant object), the errors which have frequently arisen 
from their not having been set off perpendicularly, 
where the eye has been the only criterion, are entirely 
obviated ; and this method is also entirely free from 
the objections made to the former method. 

When the centre point E cannot be seen from every 
part of the curve, so as to allow the offsets being laid 
off radially, the more usual method may be adopted 
of laying off the offsets perpendicularly to the tangent 
B F, but in this case a cross staff should always be em- 
ployed to insure accuracy, and the distances to be set 
off from the points a lt a 2 , a s , &c, will be greater than 
those employed in the previous method, and must be 
calculated from the formula 



r — y r 2 — (ja-_oi 

instead of that given at page 131. 

The third method is most applicable where the radi- 
us of the curve is small as compared with its extent, 
and is deduced from the well-known theorem, that all 
angles contained in the same segment of a circle are 
equal to one another.* The method is as follows : — 
Place a theodolite at B and another at C, the two ter- 

• Euclid, Book III, prop. 21. 



152 A TREATISE 

urinations of the straight portions of the line, setting 
the telescope of the instrument at B on C, and that at 




C on F, the point of intersection of the lines A B and 
C D produced ; then if the former be moved through 
an arc of any number of degrees, towards F, and the 
latter the same number of degrees toward B, the point 
a l7 where the lines of collimation of the two telescopes 
intersect, will be a point in the curve ; now let both 
theodolites be again moved the same number of 
degrees and in the same directions as before, and their 
axes produced, or lines of collimation, will again inter- 
sect at a 2 , another point in the curve ; and in fact, to 
whatever extent the theodolites are moved, so long as 
the arc described is equal in both, the point of their 
intersection will always be in the required curve. Or 
more generally suppose the two theodolites to be plac- 
ed as first described, and then simultaneously to com- 
mence to revolve with the same uniform angular ve- 
locity, the point of intersection of their lines of colli- 



ON LEVELLING. ' 153 

mation will describe the circular arc C, a lt a 2 , a 3 , . . 
. . B ; and in equal intervals of time, equal portions 
of the arc will be described, which will be half as great 
as the arc, which would have been described in 
the same time, by the same angular velocity, at the cen- 
tre of the circle (E) ; from which last-mentioned cir- 
cumstance, we may readily calculate the magnitude of 
the angle through which the theodolites at B and C 
must be successively moved, in order that the points 
a u a 2i a 3, & c -> a ^ which their axes intersect, may be 
at the distance .apart which it is desired that they 
should be. If r equals the radius of the curve, d the 
required distance, and (3 the angle a x B C ; then 

d rad 



2r 



==sinj3 VII. 



As an example of the application of this method, let 
r equal 20 chains, or 1320 feet, and let it be required 
to determine points in the curve at distances of about 
100 feet ; now, from the above formula we shall obtain 

Logd = 2.000000 = log 100 
Log rad =10.000000 



12.000000 
Log2r = 3.421604 == log 2640 



Log sin = 8.578396 v (3 = 2° 10' 15". 

As it would be inconvenient, however, in practice, to 
lay off so frequently as would be required, an angle 
with odd minutes and seconds, we may instead of the 
above take an angle of 2 degrees, which will make the 



154 



A TREATISE 



distance d equal 92.13 feet. Having thus determined 
the angle, and placed the theodolites as previously de- 
scribed — viz., that at B in the direction B C, and that 
at C in the direction C F — the former must be moved 
2° towards F, and the latter 2° towards B, and a stake 
driven down at their point of intersection a^ ; the 
former must then be moved 2° more towards F, and 
the latter 2° more towards B, and another stake put 
down at their point of intersection a 2 , and so on until 
the theodolite at B is brought to the direction B F, 
and that at C to the direction C B, when the whole of 
the curve will have been staked out as required, the 
stakes being 92.13 feet apart. This method, the same 
as the last, is not liable to the objections that the first 
method was, and in addition possesses the very impor- 
tant practical advantage, that its accuracy is entirely 
independent of any undulation or change of level in 
the surface of the ground, an advantage which is not 
possessed by any of the other methods which we have 
described, the whole of which would require to have 
the distances and offsets corrected in proportion to the 
slope of the surface of the ground. In a hilly country 
— and it is in such districts that curves most frequently 
occur — this circumstance will render the last-described 
method far superior to either of those which precede 
it. 

The next method which we shall give, is that de- 
scribed by Mr. Rankine, in a communication to the 
Institution of Civil Engineers, and depends on the 



ON LEVELLING. 155 

theorem* that the angle subtended by any arc of a 
circle at the centre of a circle, is double the angle sub- 
tended by the same arc at any point in the circumfer- 
ence of the circle. The method of proceeding is as 
follows : first place a theodolite at B, the point where 




the curve commences ; and then lay off from the line 
B F the angle B, calculated from formula VII. (sup- 
posing as before r to represent the radius of the curve 
and d the distance required between the points in the 
curve), and in the direction of the axis of the instru- 
ment set off the distance d, which will give the first 
point a-L in the curve ; in the same manner lay off 
from B F the angle 2 /?, and from a t set off the same 
distance d, and the point where it cuts the axis of the 
instrument produced will be the second point a 2 ; and 
.generally by laying off the angle n /?, and setting off 

* Euclid, Book III., prop. 20. 



156 A TREATISE 

from the preceding point a m the distance d, the point 
a n will be given. 

As an example of the application of this method, let 
r equal 19 chains, or 1254 feet, and d equal 100 feet ; 
then from formula VII. we obtain 

Log d= 2.000000 = log 100 
Lograd =10.000000 



12.000000 
Log2r = 3.399328 = log 2508 



Log sin j3 = 8.600672 \ • = 2° 17' 6" ; 

then having placed the theodolite at the point B. lay 
off this angle 2° 17' 6" from the line B F, and upon 
the line B a x thus obtained set off 100 feet, which will 
give the first point in the curve a x ; then with an 
angle of 4° 34' 12" or 2/3 set off another 100 feet 
from a 1? which will give the second point a 1 , and thus 
proceed until the whole extent of the curve has been 
set out. 

Having now pointed out several methods of pro- 
cedure, in setting out the curved portions of a line of 
Railway, and having stated generally their relative 
advantages and disadvantages, we must leave it to the 
person using them to determine, from the circumstances 
attending any particular instance, which of these meth- 
ods it would be preferable to employ. It may perhaps 
be necessary to add, that in passing from a curve of 
greater to one of less radius, and vice versa, or in pass- 
ing at once from a line curving in one direction to a 



ON LEVELLING. 157 

line curving in the contrary direction, or a curve of 
contrary flexure, nothing more is requisite than to set 
off the tangent line to the curve at the point where 
the alteration occurs, and then to work from that line 
as from the line A B in any of the methods given 
above. 

In conclusion, we would urge that too much care 
cannot be employed in the operations described above, 
much of the durability of the permanent way, freedom 
from jerks and uneasy motion, and also safety in trav- 
elling upon lines of Railway, depending upon the 
accuracy with which the rails are laid, the more espe- 
cially on the curved portions of the line. 



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IMMS l.l-:\'Kl.l.l ;\ 



SCIENTIFIC BOOKS 

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Weisbacli's Mechanics. 

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A MANUAL OF THE MECHANICS OE ENGINEEKING, 

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2 SCIENTIFIC BOOKS PUBLISHED BY 

Francis 9 Lowell Hydraulics. 

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LOWELL HYDRAULIC EXPERIMENTS — being a Selec- 
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tions of Pier 3, in Process of Construc- 
tion, and Steam Dredge. XIII. Foun- 
dations of Piers 5 to 18, in Process 
of Construction. XIV. False "Works, 
showing Process of Handling and Set- 
ting Stone. XV. False Works for 
Raising Iron Work of Superstructure. 
XVI. Steam Dredge used in Founda- 
tions 9 to 18. XVII. Single Bucket 
Dredge used in Foundations of Bay 
Piers. XVIII. Saws used for Cut- 
ting Piles under water. XIX. Sand 
Pump and Concrete Box. XX Ma- 
sonry Travelling Crane. 



Whipple on Bridge Building. 

8vo, Illustrated. Cloth. $4.00. 

AN ELEMENTARY AND PRACTICAL TREATISE ON 
BRIDGE BUILDING. An enlarged and improved edition of 
the Author's original work. By S. Whipple, C. E., Inventor of 
the Whipple Bridges, &c. Second Edition. 

The design has "been to develop from Fundamental Principles a system easy 
of comprehension, and such as to enable the attentive reader and student to 
judge understandingly for himself, as to the relative merits of different plans 
and combinations, and to adopt for use such as may be most suitable for the 
cases he may have to deal with. 

It is hoped the work may prove an appropriate Text-Book upon the subject 
treated of, for the Engineering Student, and a useful manual for the Practic- 
ing Engineer and Bridge Builder. 



6 SCIENTIFIC BOOKS PUBLISHED BY 

Stoney on Strains, 

New and Revised Edition, with numerous illustrations. 

Royal 8vo, 664 pp. Cloth. $12.50. 

THE THEORY OF STRAINS IN GIRDERS and Similar Struc- 
tures, with Observations on the Application of Theory to Practice, 
and Tables of Strength and other Properties of Materials. By 
Bind on B. Stoney, B. A. 



Roebling's Bridges. 

Imperial folio. Cloth. $25.00. 

LONG AND SHORT SPAN RAILWAY BRIDGES. By John 
A. Roebling, C. E. Illustrated with large copperplate engrav- 
ings of plans and views. 

list of Plates 

1. Parabolic Truss Railway Bridge. 2, 3, 4, 5, 6. Details of Parabolic 
Truss, with centre span 500 feet in the clear. 7. Plan and View of a Bridge 
over the Mississippi River, at St. Louis, for railway and common travel. 8, 9, 
10, 11, 12. Details and View of St. Louis Bridge. 13. Railroad Bridge over 
the Ohio. 



Diedriclis' Theory of Strains. 

8vo. Cloth. $5.00. 

A Compendium for the Calculation and Construction of Bridges, 
Roofs, and Cranes, with the Application of Trigonometrical 
Notes. Containing the most comprehensive information in re- 
gard to the Resulting Strains for a permanent Load, as also for 
a combined (Permanent and Rolling) Load. In two sections 
adapted to the requirements of the present time. By John Died- 
kichs. Illustrated by numerous plates and diagrams. 

" The want of a compact, universal and popular treatise on the Construc- 
tion of Roofs and Bridges — especially one treating of the influence of a varia- 
ble load — and the unsatisfactory essays of different authors on the subject, 
induced me to prepare this work." 



D. VAN NOSTRAND. 



Whilden's Strength of Materials. 

12mo. Cloth. $2.00. 

ON THE STRENGTH OF MATERIALS used in Engineering 
Construction. By J. K. Whilden. 



Campin on Iron Roofs. 

Large 8vo. Cloth. $2.00. 

ON THE CONSTRUCTION OF IRON ROOFS. A Theoretical 
and Practical Treatise. By Feaucis Campin. With wood-cuts 
and plates of Roofs lately executed. 

" The mathematical formulas are of an elementary kind, and the process 
admits of an easy extension so as to embrace the prominent varieties of iron 
truss bridges. The treatise, though of a practical scientific character, may be 
easily mastered by any one familiar with elementary mechanics and plane 
trigonometry." 

Holley's Railway Practice. 

lvol. folio. Cloth. $12.00. 

AIERICAN AND EUROPEAN RAILWAY PRACTICE, in 

i.e Economical Greneration of Steam, including the materials 
aid construction of Coal-burning Boilers, Combustion, the Varia- 
ble Blast, Yaporization, Circulation, Super-heating, Supplying 
am Heating Feed- water, &c, and the adaptation of Wood and 
Cole-burning Engines to Coal-burning ; and in Permanent Way, 
inclding Road-bed, Sleepers, Rails, Joint Fastenings, Street 
Railways, &c, &c. By Alexander L. Holley, B. P. With 77 
lithographed plates. 

" This 3 an elaborate treatise by one of our ablest civil engineers, on the con- 
struction ,nd use of locomotives, with a few chapters on the building of Rail- 
rouls. * * * All these subjects are treated by the author, who is a 
first-class lilroad engineer, in both an intelligent and intelligible manner. The 
facts and leas are well arranged, and presented in a clear and simple style, 
accompanil by beautiful engravings, and we presume the work will be regard- 
ed as indisensable by all who are interested in a knowledge of the construc- 
tion of raihads and rolling stock, or the working of locomotives." — Scientific 
American. 



8 SCIENTIFIC BOOKS PUBLISHED BY 

Henrici 5 s Skeleton Structures. 

8vo. Cloth. $1.50. 

SKELETON STKUCTUKES, especially in their Application to 
the building of Steel and Iron Bridges. By Olaus Henbici. 
"With folding plates and diagrams. 

By presenting these general examinations on Skeleton Structures, with 
particular application for Suspended Bridges, to Engineers, I venture to ex- 
press the hope that they will receive these theoretical results with some confi- 
dence, even although an opportunity is wanting to compare them with practi- 
cal results. O. H. 



Useful Information for Railway Men. 

Pocket form. Morocco, gilt, $2.00. 

Compiled by W. G. Hamilton, Engineer. Fifth edition, revised 
and enlarged. 570 pages. 

" It embodies many valuable formulae and recipes useful for railway mer, 
and, indeed, for almost every class of persons in the world. The ' informa- 
tion ' comprises some valuable formulae and rules for the construction of 
boilers and engines, masonry, properties of steel and iron, and the stren/th 
of materials generally." — Railroad Gazette, Chicago. 



Brooklyn Water Works. 

1 vol. folio. Cloth. $25.00. 

A DESCRIPTIVE ACCOUNT OF THE CONSTRUCTION OF 
THE WORKS, and also Reports on the Brooklyn, Brtford, 
Belleville, and Cambridge Pumping Engines. Prepaed and 
printed by order of the Board of Water Commissioners With 
59 illustrations. 

Contents. — Supply Ponds — The Conduit— Ridge wood Engine louse and 
Pump Well — Kidgewood Engines — Force Mains — Ridgewood iservoir — 
Pipe Distribution — Mount Prospect Reservoir — Mount Prospdt Engine 
House and Engine — Drainage Grounds — Sewerage Works — Appe&ix. 



D. VAN~ NOSTRAND. 



Kirkwood on Filtration. 

4to. Cloth. $15.00. 

EEPOET ON THE FILTEATION OF EIVEE WATEES, for 

the Supply of Cities, as practised in Europe, made to the Board 
of Water Commissioners of the City of St. Louis. By James P. 
Kirkwood. Illustrated by 30 double-plate engravings. 

Contents. — Report on Filtration — London "Works, G-eneral — Chelsea 
"Water Works and Filters — Lambeth "Water Works and Filters — Southwark 
and Vauxhall Water Works and Filters — Grand Junction Water Works and 
Filters — West Middlesex Water Works and Filters — New River Water 
Works and Filters — East London Water "Works and Filters — Leicester Water 
"Works and Filters — York Water Works and Filters — Liverpool Water Works 
and Filters — Edinburgh "Water Works and Filters — Dublin Water Works 
and Filters — Perth Water Works and Filtering Gallery — Berlin Water 
Works and Filters — Hamburg Water Works and Reservoirs — Altona Water 
Works and Filters — Tours Water Works and Filtering Canal — Angers Water 
Works and Filtering Galleries — Nantes Water Works and Filters — Lyons 
Water Works and Filtering Galleries — Toulouse Water Works and Filtering 
Galleries — Marseilles Water Works and Filters — Genoa Water Works and 
Filtering Galleries — Leghorn Water Works and Cisterns — Wakefield Water 
Works and Filters — Appendix. 



Tunner on Roll-Turning. 

1 vol. 8vo. and 1 vol. plates. $10.00. 

A TEEATISE ON EOLL-TTJENLNG FOE THE MANUFAC- 
TUEE OF IEON. By Peter Tunner. Translated and adapted. 
By John B. Pearse, of the Pennsylvania Steel Works. With 
numerous wood-cuts, 8vo., together with a folio atlas of 10 litho- 
graphed plates of Eolls, Measurements, &o. 

" We commend this book as a clear, elaborate, and practical treatise upon 
the department of iron manufacturing operations to which it is devoted. 
The writer states in his preface, that for twenty-five years he has felt the 
necessity of such a work, and has evidently brought to its preparation the 
fruits of experience, a painstaking regard for accuracy of statement, and a 
desire to furnish information in a style readily understood. The book should 
be in the hands of every one interested, either in the general practice of 
mechanical engineering, or the special branch of manufacturing operations to 
which the work relates.' -^American Artisan. 



10 SCIENTIFIC BOOKS PUBLISHED BY 

Glynn on the Power of Water. 

12mo. Cloth. $1.00. 

A TEEATISE ON THE POWER OF WATER, as applied to 
drive Elour Mills, and to give motion to Turbines and other 
Hydrostatic Engines. By Joseph Glynn, F.R. S. Third edition, 
revised and enlarged, with numerous illustrations. 



Hewson on Embankments. 

8 to. Cloth. $2.00. 

PRINCIPLES AND PRACTICE OF EMBANKING LANDS 

from River Floods, as applied to the Levees of the Mississippi. 
By William Hewson, Civil Engineer. 

" This is a valuable treatise on the principles and practice of embanking 
lands from river floods, as applied to the Levees of the Mississippi, by a highly 
intelligent and experienced engineer. The author says it is a first attempt 
to reduce to order and to rule the design, execution, and measurement of the 
Levees of the Mississippi. It is a most useful and needed contribution to 
scientific literature. — Philadelphia Evening Journal. 



Gruner on Steel. 

8vo. Cloth. $3.50. 

THE MANUFACTURE OF STEEL. By M. L. Ortjner, trans- 
lated from the French. By Lenox Smith, A. M., E. M., with an 
appendix on the Bessemer Process in the United States, by the 
translator. Illustrated by lithographed drawings and wood-cuts. 

" The purpose of the work is to present a careful, elaborate, and at the 
same time practical examination into the physical properties of steel, as well 
as a description of the new processes and mechanical appliances for its manufac- 
ture. The information which it contains, gathered from many trustworthy 
sources, will be found of much value to the American steel manufacturer, 
who may thus acquaint himself with the results of careful and elaborate ex- 
periments in other countries, -and better prepare himself for successful com- 
petition in this important industry with foreign makers. The fact that this 
volume is from the pen of one of the ablest metallurgists of the present day, 
cannot fail, we think, to secure for it a favorable consideration. — Iron Age. 



D. VAN NOSTRAND. 11 



Bauerman on Iron. 

12mo. Cloth. $2.00. 

TEEATISE ON THE METALLUBGY OF IKON. Contain- 
ing outlines of the History of Iron Manufacture, methods of 
Assay, and analysis of Iron Ores, processes of manufacture of 
Iron and Steel, etc., etc. By H. Baueeman. First American 
edition. Revised and enlarged, with an appendix on the Martin 
Process for making Steel, from the report of Abram S. Hewitt. 
Illustrated with numerous wood engravings. 

" This is an important addition to the stock of technical "works published in 
this country. It embodies the latest facts, discoveries, and processes con- 
nected with the manufacture of iron and steel, and should be in the hands of 
every person interested in the subject, as well as in all technical and scientific 
libraries." — Scientific American. 



Link and Valve Motions, by W. S. 
Auchincloss. 

8vo. Cloth. $3.00. 

APPLICATION OF THE SLIDE VALVE and Link Motion to 
Stationary, Portable, Locomotive and Marine Engines, with new 
and simple methods for proportioning the parts. By William 
S. Auchincloss, Civil and Mechanical Engineer. Designed as 
a hand-book for Mechanical Engineers, Master Mechanics, 
Draughtsmen and Students of Steam Engineering. All dimen- 
sions of the valve are found with the greatest ease by means of 
a Printed Scale, and proportions of the link determined without 
the assistance of a model. Illustrated by 37 wood-cuts and 21 
lithographic plates, together with a copperplate engraving of the 
Travel Scale. 

All the matters we have mentioned are treated with a clearness and absence 
of unnecessary verbiage which renders the work a peculiarly valuable one. 
The Travel Scale only requires to be known to be appreciated. Mr. A. writes 
so ably on his subject, we wish he had written more. London IHn~ 
gineering. 

"We have never opened a work relating to steam which seemed to us better 
calculated t6 give an intelligent mind a clear understanding of the depart- 
ment it discusses. — Scientific American. 



12 SCIENTIFIC BOOKS PUBLISHED BY 

Slide Valve by Eccentrics, by Prof. 
C, W. MacCord. 

4to. Illustrated. Cloth, $4.00. 

A PEACTICAL TEEATISE ON THE SLIDE YALYE BY 
ECCENTRICS, examining by methods, the action of the Eccen- 
tric upon the Slide Yalve, and explaining the practical proces- 
ses of laying out the movements, adapting the valve for its 
various duties in the steam-engine. For the use of Engineers, 
Draughtsmen, Machinists, and Students of valve motions in 
general. By C. TV. MacCord, A. M., Professor of Mechanical 
Drawing, Stevens' Institute of Technology, Hoboken, N J. 



Stillman's Steam-Engine Indicator. 

12mo. Cloth. $1.00. 

THE STEAM-ENGINE INDICATOR, and the Improved Mano- 
meter Steam and Yacuum Gauges ; their utility and application 
By Paul Stillman. New edition. 



Bacon's Steam-Engine Indicator. 

12mo. Cloth. $1.00. Mor. $1.50. 

A TEEATISE ON THE EICHAEDS STEAM-ENGINE IN- 
DICATOE, with directions for its use. By Charles T. Porteb,. 
Eevised, with notes and large additions as developed by Amer- 
ican Practice, with an Appendix containing useful formulae and 
rules for Engineers. By P. W. Bacon, M. E., Member of the 
American Society of Civil Engineers. Illustrated. Second Edition 

In this work, Mr. Porter's book has been taken as the basis, but Mr. Bacon 
has adapted it to American Practice, and has conferred a great boon on 
American Engineers. — Artisan. 



Bartol on Marine Boilers. 

8vo. Cloth. $1.50. 

TEEATISE ON THE MAEINE BOILEES OF THE. UNITED 
STATES. By H. B. Bahtol. Illustrated. 



D. VAN~ NOSTRAND. 13 

Gillffiore's Limes and Cements. 

Fourth Edition. Revised and Erilargd. 

8vo. Cloth. $4.00. 

PEAOTICAL TEEATISE ON LIMES, HTDEAULIO CE- 
MENTS, AND MOETAES. Papers on Practical Engineering, 
U. S. Engineer Department, No. 9, containing Eeports of 
numerous experiments conducted in New York City, during the 
years 1858 to 1861, inclusive. By Q,. A. Gillmoke, Brig-General 
U. S. Volunteers, and Major U. S. Corps of Engineers. With 
numerous illustrations. 

" This work contains a record of certain experiments and researches made 
under the authority of the Engineer Bureau of the "War Department from 
1858 to 1861, upon the various hydraulic cements of the United States, and 
the materials for their manufacture. The experiments were carefully made, 
and are well reported and compiled. ' — Journal Franklin Institute. 



Ofillmore's Coignet Beton. 

8vo. Cloth. $2.50. 

COIGNET BETON AND OTHEE AETIFICIAL STONE. By 

Q. A. Gillmoee. 9 Plates, Yiews, etc. 

This work describes with considerable minuteness of detail the several kinds 
of artificial stone in most general use in Europe and now beginning to be 
introduced in the United States, discusses their properties, relative merits, 

and cost, and describes the materials of which they are composed 

The subject is one of special and growing interest, and we commend the work, 
embodying as it does the matured opinions of an experienced engineer and 
expert. 



Williamson's Practical Tables. 

4to. Flexible Cloth. $2.50. 

PEACTICAL TABLES IN METEOEOLOGY AND HYPSO- 
METEY, in connection with the use of the Barometer. By Col. 
E. S. Williamsom, U. S. A. 



14 SCIENTIFIC B OKS PUBLISHED B T 

Williamson on the Barometer. 

4to. Cloth. $15.00. 
ON THE USE OF THE BAKOMETER ON SURVEYS AND 

RECONNAISSANCES. Part I. Meteorology in its Connec- 
tion with. Hypsometry. Part II.. Barometric Hypsometry. By 
R. S. Williamson, Bvt. Lieut-Col. U. S. A., Major Cotps of 
Engineers. With Illustrative Tables and Engravings. Paper 
No. 15, Professional Papers, Corps of Engineers. 

" San Francisco, Cal., Feb. 27, 1867. 
" Gen. A. A. Humphreys, Chief of Engineers, U. S. Army : 

" General, — I have the honor to submit to you, in the following pages, the 
results of my investigations in meteorology and hypsometry, made with the 
view of ascertaining how far the barometer can be used as a reliable instru- 
ment for determining altitudes on extended lines of survey and reconnais- 
sances. These investigations have occupied the leisure permitted me from my 
professional duties during the last ten years, and I hope the results will be 
deemed of sufficient value to have a place assigned them among the printed 
professional papers of the United States Corps of Engineers. 
" Very respectfully, your obedient servant, 

" R. S. WILLIAMSON, 
" Bvt. Lt.-Col. TJ. S. A., Major Corps of U. S. Engineers." 



Von Cotta's Ore Deposits. 

8vo. Cloth. $4.00. 
TEEATISE ON OEE DEPOSITS. By Bernhard Yon Cotta, 
Professor of Geology in the Royal School of Mines, Ereidberg, 
Saxony. Translated from the second German edition, by 
Frederick Prime, Jr., Mining Engineer, and revised by the 
author, with numerous illustrations. 
" Prof. Von Cotta of the Freiberg School of Mines, is the author of the 
best modern treatise on ore deposits, and we are heartily glad that this ad- 
mirable work has been translated and published in this country. The trans- 
lator, Mr. Frederick Prime, Jr., a graduate of Freiberg, has had in his work 
the great advantage of a revision by the author himself, who declares in a 
prefatory note that this may be considered as a new edition (the third) of his 
own book. 

" It is a timely and welcome contribution to the literature of mining in 
this country, and we are grateful to the translator for his enterprise and good 
judgment in undertaking its preparation ; while we recognize with equal cor- 
diality the liberality of the author in granting both permission and assist- 
ance." — Extract from Review in Engineering and Mining Journal. 



D. VAN JSTOSTBAJSTD. 15 

Plattner's Blow-Pipe Analysis. 

Second edition. Revised. 8vo. Cloth. $7.50. 

PLATTNEE'S MANUAL OE QUALITATIVE AND QUAN- 
TITATIVE ANALYSIS WITH THE BLOW-PIPE. From 
tlie last German edition Revised and enlarged. By Prof. Thy 
Eichter, of the Eoyal Saxon Mining Academy. Translated by 
Prof. H. B. Cornwall, Assistant in the Colnmbia School of 
Mines, New York ; assisted by John H. Caswell. Illustrated 
with eighty-seven wood-cuts and one Lithographic Plate. 560 
pages. 

" Plattner's celebrated work has long been recognized as the only complete 
book on Blow-Pipe Analysis. The fourth German edition, edited by Prof. 
Bichter, fully sustains the reputation which the earlier editions acquired dur- 
ing the lifetime of the author, and it is a source of great satisfaction to us to 
know that Prof. Kichter has co-operated with the translator in issuing the 
American edition of the work, which is in fact a fifth edition of the original 
work, being far more complete than the last German edition." — SMimari's 
Journal. 

There is nothing so complete to be found in the English language. Platt- 
ner's book is not a mere pocket edition ; it is intended as a comprehensive guide 
to all that is at present known on the blow-pipe, and as such is really indis- 
pensable to teachers and advanced pupils. 

" Mr. Cornwall's edition is something more than a translation, as it contains 
many corrections, emendations and additions not to be found in the original. 
It is a decided improvement on the work in its German dress." — Journal of 
Applied Chemistry. 



Egleston's Mineralogy. 

8vo. Illustrated with 34 Lithographic Plates. Cloth. $4.50. 

LECTUEES ON DESCEIPTIVE MINEEALOGY, Delivered 
at the School of Mines, Columbia College. By Professor T, 
Egleston. 

These lectures are what their title indicates, the lectures on Mineralogy 
delivered at the School of Mines of Columbia College. They have been 
printed for the students, in order that more time might be given to the vari- 
ous methods of examining and determining minerals. The second part has 
only been printed. The first part, comprising crystallography and physical 
mineralogy, will be printed at some future time. 



16 SCIENTIFIC BOOKS PUBLISHED BY 

Pynchon's Chemical Physics. 

New Edition. Revised and Enlarged. 

Crown 8vo. Cloth. $3.00. 

INTRODUCTION TO CHEMICAL PHYSICS, Designed for the 
Use of Academies, Colleges, and High Schools. Illustrated with 
numerous engravings, and containing copious experiments with 
directions for preparing them. By Thomas Euggles Pynchccn", 
M. A., Professor of Chemistry and the Natural Sciences, Trinity 
College, Hartford. 

Hitherto, no work suitable for general use, treating of all these subjects 
within the limits of a single volume, could be found ; consequently the atten- 
tion they have received has not been at all proportionate to their importance. 
It is believed that a book containing so much valuable information within so 
small a compass, cannot fail to meet with a ready sale among all intelligent 
persons, while Professional men, Physicians, Medical Students, Photograph- 
ers, Telegraphers, Engineers, and Artisans generally, will find it specially 
valuable, if not nearly indispensable, as a book of reference. 

" "We strongly- recommend this able treatise to our readers as the first 
work ever published on the subject free from perplexing technicalities. In 
styie it is pure, in description graphic, and its typographical appearance is 
artistic. It is altogether a most excellent work." — Eclectic Medical Journal. 

" It treats fully of Photography, Telegraphy, Steam Engines, and the 
various applications of Electricity. In short, it is a carefully prepared 
volume, abreast with the latest scientific discoveries and inventions.'' — Hartr 
ford Courant. 

Plympton's Blow-Pipe Analysis. 

12mo. Cloth. $2.00. 

THE BLOW-PIPE : A System of Instruction in its practical use 
being a graduated course of Analysis for the use of students, 
and all those engaged in the Examination of Metallic Combina- 
tions. Second edition, with an appendix and a copious index. 
By George W- Plymptok, of the Polytechnic Institute, Brooklyn. 

" This manual probably has no superior in the English language as a text- 
book for beginners, or as a guide to the student working without a teacher. 
To the latter many illustrations of the utensils and apparatus required in 
using the blow-pipe, as well as the fully illustrated description of the blow- 
pipe flame, will be especially serviceable.'' — New York Teacher. 



D. VAN NO ST RAND. 17 



TJre's Dictionary. 



Siocth Edition, 

London, 1872. 
3 vols. 8vo. Cloth, $25.00. Half Russia, $32.50. 

DICTIONARY OF ARTS, MANUFACTURES, AND MINES. 
By Andrew Uee, M.D. Sixth, edition. Edited by Robert Hunt, 
F.R.S., greatly enlarged and rewritten. 



Brande and Cox's Dictionary, 

New Edition. 

London, 1872. 

3 vols. 8vo. Cloth, $20.00. Half Morocco, $27.50. 

A Dictionary of Science, Literature, and Art. Edited by W. T. 
Brande and Rev. Geo. W. Cox. New and enlarged edition. 



Watt's Dictionary of Chemistry. 

Supplementary Volume. 

8vo. Cloth. $9.00. 

This volume brings the Record of Chemical Discovery down, to the end of 
the year 1869, including- also several additions to, and corrections of, former 
results which have appeared in 1870 and 1871. 

* # * Complete Sets of the Work, New and Revised edition, including- above 
supplement. 6 vols. 8vo. Cloth. $62.00. 



Rammelsberg's Chemical Analysis. 

8vo. Cloth. $2.25. 

GUIDE TO A COURSE OF QUANTITATIVE CHEMICAL 
ANALYSIS, ESPECIALLY OF MINERALS AND FUR- 
NACE PRODUCTS. Illustrated by Examples. By C. E. 
Rammeisberg. Translated by J. Towler, M.D. 

This work has been translated, and is now published expressly for those 
students in chemistry whose time and other studies in colleges do not permit 
them to enter upon the more elaborate and expensive treatises of Fresenius 
and others. It is the condensed labor of a master in chemistry and of a prac- 
tical analyst. 



18 SCIENTIFIC BOOKS PUBLISHED B Y 



Eliot and Storer's Qualitative 
Chemical Analysis. 

New Edition, Revised. 
12mo. Illustrated. Cloth. $1.50. 

A COMPENDIOUS MANUAL OF QUALITATIVE CHEMI- 
CAL ANALYSIS. By Charles W. Eliot and Frank H. Stoker. 
Revised with the Cooperation of the Authors, by William Rip- 
ley Nichols, Professor of Chemistry in the Massachusetts Insti- 
tute of Technology. 

" This Manual has great merits as a practical introduction to the science 
and the art of which it treats. It contains enough of the theory and practice 
of qualitative analysis, " in the wet way,'' to bring out all the reasoning in- 
volved in the science, and to present clearly to the student the most approved 
methods of the art. It is specially adapted for exercises and experiments in 
the laboratory; and yet its classifications and manner of treatment are so 
systematic and logical throughout, as to adapt it in a high degree to that 
higher class of students generally who desire an accurate knowledge of the 
practical methods of arriving at scientific facts." — Lutheran Observer. 

" We wish every academical class in the land could have the benefit of the 
fifty exercises of two hours each necessary to master this book. Chemistry 
would cease to be a mere matter of memory, and become a pleasant experi- 
mental and intellectual recreation. "We heartily commend this little volume 
to the notice of those teachers who believe in using the sciences as means of 
mental discipline." — College Courant. 



Craig's Decimal System. 

Square 32mo. Limp. 50c. 

WEIGHTS AND MEASUEES. An Account of the Decimal 

System, with Tables of Conversion for Commercial and Scientific 
Uses. By B. E. Craig, M. D. 

" The most lucid, accurate, and useful of all the hand-books on this subject 
that we have yet seen. It gives forty-seven tables of comparison between the 
English and French denominations of length, area, capacity, weight, and the 
Centigrade and Fahrenheit thermometers, with clear instructions how to use 
them ; and to this practical portion, which helps to make the transition as 
easy as possible, is prefixed a scientific explanation of the errors in the metric 
system, and how they may be corrected in the laboratory." — Nation. 



D. VAN NOSTRAND. 19 

Nugent on Optics. 

12mo. Cloth. $2.00 

TREATISE ON OPTICS ; or, Light and Sight, theoretically and 
practically treated ; with the application to Eine Art and Indus- 
trial Pursuits. By E. Nugent. With one hundred and three 
illustrations. 

" This book is. of a practical rather than a theoretical kind, and is de- 
signed to afford accurate and complete information to all interested in appli- 
cations of the science." — Bound Table. 



Barnard's Metric System. 

8vo. Brown cloth. $3.00. 

THE METKIC SYSTEM OE WEIGHTS AND MEASUEES. 
An Address delivered before the Convocation of the University of 
the State of New York, at Albany, August, 1871. By Fredeeice: 
A. P. Barnard, President of Columbia College, New York City. 
Second edition from the Eevised edition printed for the Trustees 
of Columbia College. Tinted paper. 

" It is the best summary of the arguments in favor of the metric weights 
and measures with which we are acquainted, not only because it contains in 
small space the leading facts of the case, but because it puts the advocacy of 
that system on the only tenable grounds, namely, the great convenience of a 
decimal notation of weight and measure as well as money, the value of inter- 
national uniformity in the matter, and the fact that this metric system is 
adopted and in general use by the majority of civilized nations." — The Nation. 



The Young Mechanic. 

Illustrated. 12mo. Cloth. $1.75. 

THE YOUNG MECHANIC. Containing directions for the use 
of all kinds of tools, and for the construction of steam engines 
and mechanical models, including the Art of Turning in Wood 
and Metal. By the author of "The Lathe and its Uses," etc 
From the English edition, with corrections. 



20 SCIENTIFIC BOOKS PUBLISHED BY 

Harrison's Mechanic's Tool-Book. 

12mo. Cloth. $1.50. 

MECHANIC'S TOOL BOOK, with practical rules and suggestions, 
for the use of Machinists, Iron Workers, and others. By W. B. 
Harrison, Associate Editor of the " American Artisan." Illustra- 
ted with 44 engravings. 

" This work is specially adapted to meet the wants of Machinists and work- 
ers in iron generally. It is made up of the work-day experience of an intelli- 
gent and ingenious mechanic, who had the faculty of adapting tools to various 
purposes. The practicability of his plans and suggestions are made apparent 
even to the unpractised eye by a series of well-executed wood engravings." — 
Philadelphia Inquirer. 

Pope's Modern Practice of the Elec- 
tric Telegraph. 

Eighth Edition. 8vo. Cloth $2.00. 

A Hand-book for Electricians and Operators. By Fiunk L. Pope. 
Seventh edition. Eevised and enlarged, and fully illustrated. 

Extract from Letter of Prof. Morse. 

" I have had time only cursorily to examine its contents, but this examina- 
tion has resulted in great gratification, especially at the fairness and unpre- 
judiced tone of your whole work. 

" Your illustrated diagrams are admirable and beautifully executed. 

" I think all your instructions in the use of the telegraph apparatus judi- 
cious and correct, and I most cordially wish you success." 

Extract from Letter of Prof. O. W. Hough, of the Dudley Observatory. 

" There is no other work of this kind in the English language that con- 
tains in so small a compass so much practical information in the application 
of galvanic electricity to telegraphy. It should be in the hands of every one 
interested in telegraphy, or the use of Batteries for other purposes." 



Morse's Telegraphic Apparatus. 

Illustrated. 8vo. Cloth. $2.00. 

EXAMINATION OF THE TELEGEAPHIC APPAEATUS 
AND THE PEOCESSES IN TELEGAPHY. By Samuel F. 
B. Morse, LL.D., United States Commissioner Paris Universal 
Exposition, 1867. 



2>. VAN JSTOSTRAND. 21 

Sabine's History of the Telegraph.. 

12mo. Cloth. $1.25. 

HISTORY AND PROGRESS OF THE ELECTRIC TELE- 
GRAPH, with Descriptions of some of the Apparatus. By 
Robert Sabote, C. E. Second edition, with additions. 

Contents. — L Early Observations of Electrical Phenomena. II. Tele- 
graphs by Frictional Electricity. III. Telegraphs by Voltaic Electricity. 
IV. Telegraphs by Electro-Magnetism and Magneto-Electricity. V. Tele- 
graphs now in use. VI. Overhead Lines. VII. Submarine Telegraph Lines. 
VIIL Underground Telegraphs. IX. Atmospheric Electricity. 



Haskins' Galvanometer. 

Pocket form. Illustrated. Morocco tucks. $2.00. 

THE GALVANOMETER, AND ITS USES; a Manual for 
Electricians and Students. By C. H. Haskihs. 

" We hope this excellent little work will meet with the sale its merits 
entitle it to. To every telegrapher who owns, or uses a Galvanometer, or 
ever expects to, it will be quite indispensable." — The Telegrapher. 



Oulley's Hand-Book of Telegraphy. 

8vo. Cloth. $6.00. 
A HAND-BOOK OF PRACTICAL TELEGRAPHY. By 

R. S. Culley, Engineer to the Electric and International 
Telegraph Company. Fifth edition, revised and enlarged. 



Foster's Submarine Blasting. 

4to. Cloth. $3.50. 

SUBMARINE BLASTING in Boston Harbor, Massachusetts- 
Removal of Tower and Corwin Rocks. By John G. Fosteb, 
Lieutenant-Colonel of Engineers, and Brevet Major- General, U. 
S. Army. Illustrated with seven plates. 

List of Plates. — 1. Sketch of the Narrows, Boston Harbor. 2. 
Townsend's Submarine Drilling Machine, and "Working Vessel attending. 
3. Submarine Drilling Machine employed. 4 Details of Drilling Machine 
employed. 5. Cartridges and Tamping used. 6. Fuses and Insulated Wires 
used. 7. Portable Friction Battery used. 



22 SCIENTIFIC BOOKS PUBLISHED BY 

Barnes' Submarine Warfare. 

8vo. Cloth. $5.00. 

SUBMARINE WARFARE, DEFENSIVE AND OFFENSIVE. 

Comprising a full and complete History of the Invention of the 
Torpedo, its employment in War and results of its use. De- 
scriptions of the various forms of Torpedoes, Submarine Batteries 
and Torpedo Boats actually used in War. Methods of Ignition 
by Machinery, Contact Fuzes, and Electricity, and a full account 
of experiments made to determine the Explosive Force of Gun- 
powder under Water. Also a discussion of the Offensive Torpedo 
system, its effect upon Iron-Clad Ship systems, and influence upon 
Future Naval Wars. By Lieut.-Commander John S. Bakstes, 
U. S. N. With twenty lithographic plates and many wood-cuts. 

" A book important to military men, and especially so to engineers and ar- 
tillerists. It consists of an examination of the various offensive and defensive 
engines that have been contrived for submarine hostilities, including a discus- 
sion of the torpedo system, its effects upon iron-clad ship-systems, and its 
probable influence upon future naval wars. Plates of a valuable character 
accompany the treatise, "which affords a useful history of the momentous sub- 
ject it discusses. A great deal of useful information is collected in its pages, 
especially concerning the inventions of Scholl and Verdu, and of Jones' 
and Hunt's batteries, as well as of other similar machines, and the use in 
submarine operations of gun-cotton and nitro-glycerine." — N. T. Times. 



Randall's Quartz Operator's Hand- 

Book. 

12mo. Cloth. $2.00. 

QUARTZ OPERATOR'S HAND-BOOK. By P. M. Randall. 
New edition, revised and enlarged. Fully illustrated. 

The object of this work has been to present a clear and comprehensive ex- 
position of mineral veins, and the means and modes chiefly employed for the 
mining and working of their ores — more especially those containing gold and 
silver. 



B. VAN NOSTRAND. 23 



Mitchell's Manual of Assaying. 

8vo. Cloth. $10.00. 

A MANUAL OF PEACTICAL ASSAYING. By John Mitchell. 
Third edition. Edited by William Chookes, E.B.S. 

In this edition are incorporated all the late important discoveries in Assay- 
ing made in this country and abroad, and special care is devoted to the very 
important Volumetric and Oolorimetric Assays, as well as to the Blow-Pipe 

Assays. 



Benet's Chronoscope. 

Second Edition. 

Illustrated. 4to. Cloth. $3.00. 

ELECTEO-BALLISTIO MACHINES, and the Schultz Chrono- 
scope. By Lieutenant-Colonel S. V. Benet, Captain of Ordnance, 
U. S. Army. 

Contents. — 1. Ballistic Pendulum. 2. G-un Pendulum. 3. Use of Elec- 
tricity. 4. Navez' Machine. 5. Vignotti's Machine, with Plates. 6. Benton's 
Electro-Ballistic Pendulum, with Plates. 7. Leur's Tro-Pendulum Machine 
8. Schultz's Chronoscope, with two Plates. 



Michaelis' Chronograph. 

4to. Illustrated. Cloth. $3.00. 

THE LE BOULENGfi CHKONOGKAPH. With three litho- 
graphed folding plates of illustrations. By Brevet Captain E. 
Michaelis, First Lieutenant Ordnance Corps, U. S. Army. 

" The excellent monograph of Captain Michaelis enters minutely into the 
details of construction and management, and gives tables of the times of flight 
calculated upon a given fall of the chronometer for all distances. Captain 
Michaelis has done good service in presenting this work to his brother officers, 
describing, as it does, an instrument which bids fair to be in constant use in 
our future ballistic experiments.' — Army and Navy Journal. 



24 SCIENTIFIC BOOKS PUBLISHED Br 



Silversmith's Hand-Book. 

Fourth Edition. 

Illustrated. 12mo. Cloth. $3.00. 

A PRACTICAL HAND-BOOK TOR MINERS, Metallurgists, 
and Assayors, comprising tho most recent improvements in the 
disintegration, amalgamation, smelting, and parting of the 
Precious Ores, with a Comprehensive Digest of the Mining 
Laws. Greatly augmented, revised, and corrected. By Julius 
Siltbbsmith. Fourth edition. Profusely illustrated. 1 vol. 
12mo. Cloth. $3.00. 

Ono of the most important features of this work is that in which the 
metallurgy of tho proeious motals is treated of. In it the author has endeav- 
ored to embody all the processes for the reduction and manipulation of tho 
precious ores heretofore successfully employed in Germany, England, Mexico, 
and the United States, together with such as have been more recently invented, 
and not yet fully tested — all of which aro profusely illustrated and easy of 
comprehension. 



Simms' Levelling. 

8vo. Cloth. $2.50. 

A TBEATISE ON THE PRINCIPLES AND PRACTICE OF 
LEVELLING, showing, its application to purposes of Railway 
Engineering and tho Construction of Roads, &c. By Fbedeeick 
W. Simms, ( !. E. From tho fifth London edition, revised and 
corrected, with tho addition of Mr. Law's Practical Examples for 
Setting Out Railway Curves. Illustrated with three lithographic 
plates and numerous wood-cuts. 

" One of tho most important text-books for tho general surveyor, and there 
is soarcoly a question connected with levelling for which a solution would be 
sought, but that would bo satisfactorily answerod by consulting this volume." 
— Mining Journal. 

" The text-book on lovolling in most of our engineering schools and col- 
legos." — Engineers. 

"Tho publishers have renderod a substantial service to the profession* 
especially to the younger members, by bringing out the present edition of 
Mr. Simms usoful work." — Engineering. 



D. VAN JSTOSTBAND. 25 



Stuart's Successful Engineer. 

18mo. Boards. 50 cents. 
HOW TO BECOME A SUCCESSFUL ENGINEER: Being 

Hints to Youths intending to adopt the Profession. By 

Bernard Stuart, Engineer. Sixth Edition. 

"A valuable little book of sound, sensible advice to young men who 
wish to rise in the most important of the professions."— Scientific American. 



Stuart's Naval Dry Docks. 

Twenty-four engravings on steel. 
Fourth Edition, 

4to. Cloth. $6.00. 

THE NAVAL DRY DOCKS OF THE UNITED STATES. 
By Chaeles B. Sttjaet. Engineer in Chief of the United States 
Navy. 

List of Illustrations. 

Pumping Engine and Pumps — Plan of Dry Dock and Pump-Well— Sec- 
tions of Dry Dock — Engine House — Iron Floating Gate — Details of Floating 
Gate — Iron Turning Gate — Plan of Turning Gate — Culvert Gate — Filling 
Culvert Gates — Engine Bed — Plate, Pumps, and Culvert — Engine House 
Roof — Floating Sectional Dock — Details of Section, and Plan of Turn-Tables 
— Plan of Basin and Marine Railways — Plan of Sliding Frame, and Elevation 
of Pumps — Hydraulic Cylinder — Plan of Gearing for Pumps and End Floats 
— Perspective View of Dock, Basin, and Railway — Plan of Basin of Ports- 
mouth Dry Dock — Floating Balance Dock— Elevation of Trusses and the Ma- 
chinery—Perspective View of Balance Dry Dock 



Free Hand Drawing. 

Profusely Illustrated. 18mo. Boards. 50 cents* 

A GUIDE TO ORNAMENTAL, Figure, and Landscape Draw- 
ing. By an. Art, Student. 

Contents. — Materials employed in Drawing, and how to use them — On 
Lines and how to Draw them — On Shading — Concerning lines and shading, 
with applications of them to simple elementary subjects — Sketches from Na- 
ture. 



26 SCIENTIFIC BOOKS PUBLISHED BY 



Minifie's Mechanical Drawing. 

Eighth Edition. 

Royal 8vo. Cloth. $4.00. 

A TEXT-BOOK OF GEOMETEICAL DEAWING for the use 

of Mechanics and Schools, in which the Definitions and Rules of 
Geometry are familiarly explained ; the Practical Problems are 
arranged, from the most simple to the more complex, and in their 
description technicalities are avoided as much as possible. With 
illustrations for Drawing Plans, Sections, and Elevations of 
Buildings and Machinery ; an Introduction to Isometrical Draw- 
ing, and an Essay on Linear Perspective and Shadows. Illus- 
trated with over 200 diagrams engraved on steel. By Wi. 
Minifie, Architect. Eighth Edition. With an Appendix on the 
Theory and Application of Colors. 

" It is tke best work on Drawing- that we have ever seen, and is especially a 
text-book of Geometrical Drawing for the use of Mechanics and Schools. No 
young Mechanic, such as a Machinist, Engineer, Cabinet-Maker, Millwright, 
or Carpenter, should be without it." — Scientific American. 

" One of the most comprehensive works of the kind ever published, and can- 
not but possess great value to builders. The style is at once elegant and sub- 
stantial. " — Pennsylvania Inquirer. 

" Whatever is said is rendered perfectly intelligible by remarkably well- 
executed diagrams on steel, leaving nothing for mere vague supposition ; and 
the addition of an introduction to isometrical drawing, linear perspective, and 
the projection of shadows, winding up with a useful index to technical terms." 
— Glasgow Mechanics' 1 Journal. 

^W The British Government has authorized the use of this book in their 
schools of art at Somerset House, London, and throughout the kingdom. 



Minifie's Geometrical Drawing. 

New Edition. Enlarged. 

12mo. Cloth. $2.00. 

GEOMETEICAL DEAWING. Abridged from the octavo edition, 
for the use of Schools. Illustrated with 48 steel plates. New 
edition, enlarged. 

l ' It is well adapted as a text-book of drawing to be used in our High Schools 
and Academies where this useful branch of the fine arts has been hitherto too 
much neglected." — Boston Journal. 



D. VAN NOSTBANB. 27 



Bell on. Iron Smelting. 

8vo. Cloth. $6.00. 

CHEMICAL PHENOMENA OF IEON SMELTING. An ex- 
perimental and practical examination of the circumstances which 
determine the capacity of the Blast Eurnace, the Temperature 
of the Air, and the Proper Condition of the Materials to be 
operated upon. By I. Lowthian Bell. 

" The reactions which take place in every foot of the blast-furnace have 
been investigated, and the nature of every step in the process, from the intro- 
duction of the raw material into the furnace to the production of the pig iron, 
has been carefully ascertained, and recorded so fully that any one in the trade 
can readily avail themselves of the knowledge acquired ; and we have no hes- 
itation in saying that the judicious application of such knowledge will do 
much to facilitate the introduction of arrangements which will still further 
economize fuel, and at the same time permit of the quality of the resulting 
metal being maintained, if not improved. The volume is one which no prac- 
tical pig iron manufacturer can afford to be without if he be desirous of en- 
tering upon that competition which nowadays is essential to progress, and 
in issuing such a work Mr. Bell has entitled himself to the best thanks of 
every member of the trade." — London Mining Journal. 



Zing's Notes on Steam. 

Thirteenth Edition* 

8vo. Cloth. $2.00. 

LESSONS AND PRACTICAL NOTES ON STEAM, the Steam- 
Engine, Propellers, &c, &c, for Young Engineers, Students, and 
others. By the late W. R. King, U. S. N. Revised by Chief- 
Engineer J. W. King, U. S. Navy. 

" This is one of the best, because eminently plain and practical treatises on 
the Steam Engine ever published. ' — Philadelphia Press. 

This is the thirteenth edition of a valuable work of the late W. H. King, 
TJ. S. N. It contains lessons and practical notes on Steam and the Steam En- 
gine, Propellers, etc. It is calculated to be of great use to young marine en- 
gineers, students, and others. The text is illustrated and explained by nu- 
merous diagrams and representations of machinery.— Boston Daily Adver- 
tiser. 

Text-book at the TJ. S. Naval Academy, Ann apolis. 



28 SCIENTIFIC BOOKS PUBLISHED B Y v 

Burgh's Modern Marine Engineering. 

One thick 4to vol. Cloth. $25.00. Half morocco. $30.00. 

MODEEN MAEINE ENGINEERING, applied to Paddle and 
Screw Propulsion. Consisting of 36 Colored Plates, 259 Practical 
Wood-cut Illustrations, and 403 pages of Descriptive Matter, the 
whole being an exposition of the present practice of the follow- 
ing firms : Messrs. J. Penn & Sons ; Messrs. Maudslay, Sons & 
Field ; Messrs. James Watt & Co. ; Messrs. J. & G. Eennie ; 
Messrs. E. Napier & Sons ; Messrs. J. & W. Dudgeon ; Messrs. 
Eavenhill & Hodgson ; Messrs. Humphreys & Tenant ; Mr. 
J. T. Spencer, and Messrs. Forrester & Co. By N. P. Bukgh, 
Engineer. 

Principal Contents. — General Arrangements of Engines, 11 examples 
— General Arrangement of Boilers, 14 examples — General Arrangement of 
Superheaters, 11 examples — Details of 'Oscillating Paddle Engines, 04 ex- 
amples — Condensers for Screw Engines, both Injection and Surface, 20 ex- 
amples — Details of Screw Engines, 20 examples — Cylinders and* Details of 
Screw Engines, 21 examples — -Slide Valves and Details, 7 examples — Slide 
Valve, Link Motion, 7 examples — Expansion Valves and Gear, 10 exam- 
ples — Details in General, 30 examples --Screw Propeller and Fittings, 13 ex- 
amples Engine and Boiler Fittings, 28 examples - In relation to the Princi- 
ples of the Marine Engine and Boiler, 33 examples. 

Notices of the Press. 

"Every conceivable detail of the Marine Engine, under all its various 
forms, is profusely, and we must add, admirably illustrated by a multitude 
of engravings, selected from the best and most modern practice of the first 
Marine Engineers of the day. The chapter on Condensers is peculiarly valu- 
able. In one word, there is no other work in existence which will bear a 
moment's comparison with it as an exponent of the skill, talent and practical 
experience to which is due the splendid reputation enjoyed by many British 
Marine Engineers." — Engineer. 

" This very comprehensive work, which was issued in Monthly parts, has 
just been completed. It contains large and full drawings and copious de- 
scriptions of most of the best examples of Modern Marine Engines, and it is 
a complete theoretical and practical treatise on the subject of Marine Engi- 
neering."— American Artisan. 

This is the only edition of thn above work with the beautifully colored 
plates, and it is out of print in England. 



-, -- ,-■ 



D. VAJST NOSTHAN-D. 29 

Bourne's Treatise on the Steam En- 
gine. 

Ninth Edition. 

Illustrated. 4to. Cloth. $15.00. 
TREATISE ON THE STEAM ENGINE in its various applica- 
tions to Mines, Mills, Steam Navigation, Railways, and Agricul- 
ture, with the theoretical investigations respecting the Motive 
Power of Heat and the proper Proportions of Steam Engines. 
Elaborate Tables of the right dimensions of every part, and 
Practical Instructions for the . Manufacture and Management of 
every species of Engine in actual use. By John BottkjSTe, being 
the ninth edition of "A Treatise on the Steam Engine," by 
the " Artisan Club." Illustrated by thirty-eight plates and five 
hundred and forty-six wood-cuts. 

As Mr. Bourne's work has the great merit of avoiding unsound and imma- 
ture views, it may safely be consulted by all who are really desirous of ac- 
quiring trustworthy information on the subject of which it treats. During 
the twenty-two years which have elapsed from the issue of the first edition, 
the improvements introduced in the construction of the steam engine have 
been both numerous and important, and of these Mr. Bourne has taken care 
to point out the more prominent, an4 to furnish the reader with such infor- 
mation as shall enable him readily to judge of their relative value. This edi- 
tion has been thoroughly modernized, and made to accord with the opinions 
and practice of the more successful engineers of the present day. All that 
the book professes to give is given with ability and evident care. The scien- 
tific principles which are permanent are admirably explained, and reference 
is made to many of the more valuable of the recently introduced engines. To 
express an opinion of the value and utility of such a work as The Artisan 
Club's Treatise on the Steam Engine, which has passed through eight editions 
already, would be superfluous ; but it may be safely stated that the work is 
worthy the attentive study of all either engaged in the manufacture of steam 
engines or interested in economizing the use of steam. — Mining Journal. 



Isherwood's Engineering Precedents. 

Two Vols, in One. 8vo. Cloth. $2.50. 

ENGINEERING PRECEDENTS FOR STEAM MACHINERY. 

Arranged in the most practical and useful manner for Engineers. 
By B. I\ Isherwood, Civil Engineer, U. S. Navy. With illus- 
trations. 



30 SCIENTIFIC BOOKS PUBLISHED BY 



Ward's Steam for the Million. 

New and Revised Edition. 

8vo. Cloth. $1.00. 

STEAM FOE THE MILLION. A Popular Treatise on Steam 
and its Application to the Useful Arts, especially to Naviga- 
tion. By J. H. Wakd, Commander U. S. Navy. New and re- 
vised edition. 

A most excellent work for the young engineer and general reader. Many 
facts relating to the management of the*boiler and engine are set forth with a 
simplicity of language and perfection of detail that bring the subject home 
to the reader. — American Engineer. 



Walker's Screw Propulsion. 

8vo. Cloth. 75 cents. 

NOTES ON SCEEW PEOPULSION, its Eise and History. By 
Oapt. W. H. Walker, U. S. Navy. 

Commander Walker's book contains an immense amount of concise practi- 
cal data, and every item of information recorded fully proves that the various 
points bearing upon it have been well considered previously to expressing an 
opinion. — London Mining Journal. 



Page's Earth's Crust. 

18mo. Cloth. 75 cents. 

THE EAETH'S CEUST : a Handy Outline of Geology. By 
David Page. 

" Such a work as this was much wanted — a work giving in clear and intel- 
ligible outline the leading facts of the science, without amplification or irk- 
some details. It is admirable in arrangement, and clear and easy, and, at the 
same time, forcible in style. It will lead, we hope, to the introduction of 
G eology into many schools that have neither time nor room for the study of 
largre treatises." — The Museum. 



D. VAN JVOSTHAJSTD. 31 

Rogers 5 Geology of Pennsylvania. 

3 Vols. 4to, with Portfolio of Maps. Cloth. $30.00. 

THE GEOLOGY OF PENNSYLVANIA. A Government Sur- 
vey. With a general view of the Geology of the United States, 
Essays on the Coal Formation and its Fossils, and a description 
of the Coal Fields of North America and Great Britain. By 
Henry Darwin Rogers, Late State Geologist of Pennsylvania. 
Splendidly illustrated with Plates and Engravings in the Text. 

It certainly should be in every public library „nroughout the country, and 
likewise in the possession of all students of G-eology. After the final sale of 
these copies, the work will, of course, become more valuable. 

The work for the last five years has been entirely out of the market, but a 
few copies that remained in the hands of Prof. Rogers, in Scotland, at the 
time of his death, are now offered to the public, at a price which is even 
below what it was originally sold for when first published. 



Morfit on Pure Fertilizers. 

With 28 Illustrative Plates. 8vo. Cloth. $20.00. 

A PEACTICAL TEEATISE ON PURE FERTILIZERS, and 

the Chemical Conversion of Rock Guanos, Marlstones, Coprolites, 
and the Crude Phosphates of Lime and Alumina Generally, into 
various Valuable Products. By Campbell Morfit, M.D., F.C.S. 



Sweet's Report on Coal. 

8vo. Cloth. $3.00. 

SPECIAL REPORT ON COAL • showing its Distribution, Classi- 
fication, and Cost delivered over different routes to various points 
in the State of New York, and the principal cities on the Atlantic 
Coast. By S. H. Sweet. With maps. 



Colburn 5 s Gas Works of London. 

12mo. Boards . 60 cents. 
GAS WORKS OF LONDON. By Zee^h Colettes 



I 



32 SCIENTIFIC BOOKS PUBLISHED BY 

The Useful Metals and their Alloys ; 
Scoffren, Truran, and others. 

Fifth Edition, 

8vo. Half calf. $3.75. 
THE USEFUL METALS AND THEIE ALLOYS, including 
MINING VENTILATION, MINING JUEISPEUDENCE 
AND METALLUEGIC CHEMISTEY employed in the conver- 
sion of IEON, COPPEE, TIN, ZINC, ANTIMONY, AND 
LEAD OEES, with their applications to THE INDUSTEIAL 
AETS. By John Scoffren, William Tehran, William Clay, 
Eobert Oxland, William Fairbairn, W. C. Aitkin, and Wil- 
liam Yose Pickett. 



Collins' Useful Alloys. 

18mo. Flexible. 75 cents. 

THE PEIYATE BOOK OF USEFUL ALLOYS and Memo- 
randa for Goldsmiths, Jewellers, etc. By James E. Collins 

This little book is compiled from notes made by the Author from the 
papers of one of the largest and most eminent Manufacturing Goldsmiths and 
Jewellers in this country, and as the firm is now no longer in existence, and the 
Author is at present engaged in some other undertaking, he now offers to the 
public the benefit of his experience, and in so doing he begs to state that all 
the alloys, etc., given in these pages may be confidently relied on as being 
thoroughly practicable. 

The Memoranda and Receipts throughout this book are also compiled 
from practice, and will no doubt be found useful to the practical jeweller. 
—Shirley, July, 1871. 

Joynson s Metals Used in Construction. 

12mo. Cloth. 75 cents. 

THE METALS USED IN CONSTEUCTION : Iron, Steel, 
Bessemer Metal, etc., etc. By Francis Herbert Joynson. Il- 
lustrated. 

" In the interests of practical science, we are bound to notice this work ; 
and to those who wish further information, we should say, buy it ; and the 
outlay, we honestly believe, will be considered well spent." — Scientific 
Review. 



D. VAN NOSTltANB. 33 



Holley's Ordnance and Armor. 

493 Engravings. Half Roan, $10.00. Half Russia, $12.00. 

A TKEATISE ON OEDNANCE AND AEM OB— Embracing 

Descriptions, Discussions, and Professional Opinions concerning 
the Material, Fabrication, Eequirements, Capabilities, and En- 
durance of European and American Guns, for Naval, Sea Coast, 
and Iron-clad Warfare, and their Bifling, Projectiles, and 
Breech-Loading; also, Eesults of Experiments against Armor, 
from Official Eecords, with an Appendix referring to Grun-Cotton, 
Hooped Guns, etc., etc. By Alexander L. Hollev, B. P. 948 
pages, 493 Engravings, and 147 Tables of Eesults, etc. 

Contents. 

Chapter I. — Standard G-uns and their Fabrication Described : Section 1. 
Hooped Guns ; Section 2. Solid "Wrought Iron Guns ; Section 3. Solid Steel 
Guns ; Section 4. Cast-Iron Guns. Chapter II. — The Requirements of Guns, 
Armor: Section 1. The Work to be done ; Section 2. Heavy Shot at Low Ve- 
locities ; Section 3. Small Shot at High Velocities ; Section 4. The two Sys- 
tems Combined; Section 5. Breaching Masonry. Chapter III. — The Strains 
and Structure of Guns: Section 1. Resistance to Elastic Pressure; Section 2. 
The Effects of Vibration; Section 3. The Effects of Heat. Chapter IV.— 
Cannon Metals and Processes of Fabrication: Section 1. Elasticity and Ductil- 
ity; Section 2. Cast-iron; Section 3. "Wrought Iron; Section 4. Steel; Sec- 
tion 5. Bronze ; Section 6. Other Alloys. Chapter V. — Rifling and Projec- 
tiles ; Standard Forms and Practice Described ; Early Experiments ; The 
Centring System ; The Compressing System ; The Expansion System ; Armor 
Punching Projectiles ; Shells for Molten Metal ; Competitive Trial of Rifled 
Guns, 1862; Duty of Rifled Guns: General Uses, Accuracy, Range, Velocity, 
Strain, Liability of Projectile to Injury ; Firing Spherical Shot from Rifled 
Guns; Material for Armor-Punching Projectiles; Shape of Armor-Punching 
Projectiles; Capacity and Destructiveness of Shells; Elongated Shot from 
Smooth Bores; Conclusions; Velocity of Projectiles (Table \ Chapter VI. — 
Breech-Loading Advantages and Defects of the System; Rapid Firing and 
Cooling Guns by Machinery ; Standard Breech-Loaders Described. Part Sec- 
ond : Experiments against Armor ; Account of Experiments from Official 
Records in Chronological Order. Appendix. — Report on the Application of 
Gun-Cotton to "Warlike Purposes — British Association, 1863; Manufacture and 
Experiments in England ; Guns Hooped with Initial Tension — History; How 
Guns Burst, by "Wiard, Lyman's Accelerating Gun; Endurance of Parrott 
and "Whitworth Guns at Charleston ; Hooping old United States Cast-Iron 
Guns ; Endurance and Accuracy of the Armstrong 600-pounder; Competitive 
Trials with 7-inch Guns. 



34 SCIENTIFIC BOOKS PUBLISHED BY 

Peirce's Analytic Mechanics. 

4to. Cloth. $10.00. 

SYSTEM OF ANALYTIC MECHANICS. Physical and Celestial 
Mechanics. By Benjamin Peir.ce, Perkins Professor of Astronomy 
and Mathematics in Harvard University, and Consulting As- 
tronomer of the American Ephemeris and Nautical Almanac. 
Developed in four systems of Analytic Mechanics, Celestial 
Mechanics, Potential Physics, and Analytic Morphology. 

" I have re-examined the memoirs of the great geometers, and have striven 
to consolidate their latest researches and their most exalted forms of thought 
into a consistent and uniform treatise. If I have hereby succeeded in open- 
ing to the students of my country a readier access to these choice jewels of 
intellect ; if their brilliancy is not impaired in this attempt to reset them ; if, 
in their own constellation, they illustrate each other, and concentrate 
a stronger light upon the names of their discoverers , and, still more, if any 
gem which I may have presumed to add is not wholly lustreless in the collec- 
tion, I shall feel that my work has not been in vain."— Extract from the Pre- 
face. 

Burt's Key to Solar Compass. 

Second Edition. 

Pocket Book Form. Tuck. $2.50. 

KEY TO THE SOLAR COMPASS, and Surveyor's Companion ; 
comprising all the Pules necessary for use in the field; also, 
Description of the Linear Surveys and Public Land System of 
the United States, Notes on the Barometer, Suggestions for an 
outfit for a Survey of four months, etc., etc., etc. By W. A. 
Burt, U. S. Deputy Surveyor. Second edition. 



Cliauvenet's Lunar Distances. 

8vo. Cloth. $2.00. 

NEW METHOD OF CORRECTING LUNAR DISTANCES, 
and Improved Method of Finding the Error and Rate of a Chro- 
nometer, by equal altitudes. By Wi. Chauvenet, LL.D., Chan- 
cellor of Washington University of St. Louis. 



J). VAN NOSTRAND. 35 



Jeffers 9 Nautical Surveying. 

Illustrated with 9 Copperplates and 31 Wood-cut Illustrations. 8vo. 
Cloth. $5.00. 

NAUTICAL SURVEYING. By William N. Jeffees, Captain 
U. S. Navy. 

Many books have been written on each of the subjects treated of in the 
sixteen chapters of this work; and, to obtain a complete knowledge of 
geodetic surveying requires a profound study of the whole range of mathe- 
matical and physical sciences ; but a year of preparation should render any 
intelligent officer competent to conduct a nantical survey. 

Contents. — Chapter I. Eormuhe and Constants Useful in Surveying 
II. Distinctive Character of Surveys. III. Hydrographic Surveying under 
Sail ; or, Running Survey. IV. Hydrographic Surveying of Boats ; or, Har- 
bor Survey. V. Tides — Definition of Tidal Phenomena — Tidal Observations. 
VI. Measurement of Bases — Appropriate and Direct. VII. Measurement of 
the Angles of Triangles — Azimuths — Astronomical Bearings. VIII. Correc- 
tions to be Applied to the Observed Angles. IX. Levelling — Difference of 
Level. X. Computation of the Sides of the Triangulation — The Three-point 
Problem. XL Determination of the G-eodetic Latitudes, Longitudes, and 
Azimuths, of Points of a Triangulation. XII. Summary of Subjects treated 
of in preceding Chapters — Examples of Computation by various Formulae. 
XIII. Projection of Charts and Plans. XIV. Astronomical Determination of 
Latitude and Longitude. XV. Magnetic Observations. XVI. Deep Sea 
Soundings. XVII. Tables for Ascertaining Distances at Sea, and a full 
Index. 

List of Plates. 

Plate I. Diagram Illustrative of the Triangulation. II. Specimen Page 
of Field Book. III. Punning Survey of z. Coast. IV. Example of a Running 
Survey from Belcher. V. Flying Survey of an Island. VI. Survey of a 
Shoal. VII. Boat Survey of a River. VIII. Three-Point Problem. IX. 
Triangulation. 

Coffin's Navigation. 

Fifth Edition. 

12mo. Cloth. $3.50. 

NAVIGATION AND NAUTICAL ASTEONOMY. Prepared 
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Clark's Theoretical Navigation. 

8vo. Cloth. $3.00. 

THEORETICAL NAVIGATION AND NAUTICAL ASTEON- 

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Prepared for Use at the U. S. Naval Academy. 



The Plane Table. 

Illustrated. 8vo. Cloth. $2.00. 

ITS USES IN TOPOGEAPHICAL SUEVEYING. From the 
Papers of the U. S. Coast Survey. 

This work gives a description of the Plane Table employed at the U. S. 
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Pook on Shipbuilding. 

8vo. Cloth. $5.00. 

METHOD OF COMPAEING THE LINES AND DEAUGHT- 
ING VESSELS PEOPELLED BY SAIL OE STEAM, in- 
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Brunnow's Spherical Astronomy, 

8vo. Cloth. $6.50. 

SPHEEICAL ASTEONOMY. By F. Beunnow, Ph. Dr. Trans- 
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D. VAN NO&TRAND. 37 

Van Buren's Formulas. 

8vo. Cloth. $2.00. 

INVESTIGATIONS OE FOKMTJLAS, for the Strength of the 
Iron Parts of Steam Machinery. By J. D. Van Buren, Jr., 0. E. 
Illustrated. 

This is an analytical discussion of the formulae employed hy mechanical 
engineers in determining the rupturing or crippling pressure in the different 
parts of a machine. The formulae are founded upon the principle, that the 
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Joynson on Machine Gearing. 

8vo. Cloth. $2.00. 

THE MECHANIC'S AND STUDENT'S GUIDE in the Design- 
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and Curved Surfaces ; with Practical Rules and Details. Edited 
by Francis Herbert Joynson. Illustrated with 18 folded 
plates. 

" The aim of this work is to he a guide to mechanics in the designing and 
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Barnard's Report, Paris Exposition, 

1867. 

Illustrated. 8vo. Cloth. $5.00. 

EEPOET ON MACHINEEY AND PEOCESSES ON THE 
INDUSTRIAL AETS AND APPAEATUS OF THE EXACT 
SCIENCES. By F. A. P. Barnard, LL.D.— Paris Universal 
Exposition, 1867. 

" We have in this volume the results of Dr. Barnard's study of the Paris 
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since the Universal Exhibition of 1851, and we doubt if anything equal to it 
has appeared this century."— Journal Applied Chemistry. 



38 SCIENTIFIC BOOKS PUBLISHED BY 

Engineering Facts and Figures. 

18mo. Cloth. $2.50 per Volume. 

AN ANNUAL EEGISTEE OF PEOGEESS IN MECHANI- 
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Each volume sold separately. 



Beckwith's Pottery. 

8vo. Paper. 60 cents. 

OBSEEVATIONS ON THE MATERIALS and Manufacture of 
Terra-Cotta, Stone- Ware, Fire-Brick, Porcelain and Encaustic 
Tiles, with Remarks on the Products exhibited at the London 
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Engineer. 

" Everything" is noticed in this book which comes under the head of Pot- 
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Dodd's Dictionary of Manufactures, etc. 

12mo. Cloth. $2.00. 

DICTIONAEY OF MANUFACTUEES, MINING, MACHIN- 
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This work, a small book on a great subject, treats, in alphabetical ar- 
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as subjects of natural history. The operations of the Mine and the Mill, the 
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is indicated in various ways. 



D. VAN NOSTRANB. 39 

Stuart's Civil and Military Engineer- 
ing of America. 

8vo. Illustrated. Cloth. $5.00. 

THE CIVIL AND MILITAEY ENGINEEKS OF AMEEICA. 

By General Charles B. Stuart, Author of " Naval Dry Docks 
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Containing sketches of the Life and "Works of Major Andrew Ellicott, 
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trait), Jonathan Knight, Benjamin H. Latrobe (with Portrait), Colonel Char- 
les Ellet, Jr. with Portrait), Samuel Porrer, William Stuart Watson, John 
A. Roebling. 



Alexander's Dictionary of Weights 
and Measures. 

8vo. Cloth. $3.50. 

UNIVEKSAL DICTIONABY OF WEIGHTS AND MEAS- 
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United States of America. By J. H. Alexander. New edition, 
lvol. 

"Asa standard work of reference, this book should be in every library ; it 
is one which we have long wanted, and it will save much trouble and re- 
search." — Scientific American. 



Gonge on Ventilation. 

Third Edition Enlarged. 

8vo. Cloth. $2.00. 
NEW SYSTEM OF VENTILATION, which has been thoroughly 
tested under the patronage of many distinguished persons. By 
Henry A. Gouge, with many illustrations. 



40 SCIENTIFIC BOOKS PUBLISHED BY 



Saeltzer's Acoustics. 

12mo. Cloth. $2.00. 

TREATISE ON ACOUSTICS in Connection with Ventilation. 
With a new theory based on an important discovery, of facilitat- 
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Saeltzer. 

" A practical and very sound treatise on a subject of great importance to 
architects, and one to -which there has hitherto "been entirly too little attention 
paid. The author's theory is, that, by bestowing proper care upon the point 
of Acoustics, the requisite ventilation will be obtained, and vice versa. — 
Brooklyn Union. 



Myer's Manual of Signals. 

New Edition. Enlarged. 

12mo. 48 Plates full Roan. $5.00. 

MANUAL OF SIGNALS, for the Use of Signal Officers in the 
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etc. A new edition, enlarged and illustrated. By Brig. -Gen. 
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the Signal Corps during the War of the Rebellion. 



Larrabee's Secret Letter and 
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18mo. Cloth. $1.00. 

CIPHER AND SECRET LETTER AND TELEGRAPHIC 

CODE, with Hogg's Improvements. The most perfect secret 
Code ever invented or discovered. Impossible to read without 
the Key. Invaluable for Secret, Military, Naval, and Diplo- 
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D. VAN NOSTRAND. 4i 



Hunt's Designs for Central Park 
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4to. Cloth. $5.00. 

DESIGNS FOR THE GATEWAYS OF THE SOUTHERN 
ENTRANCES TO THE CENTRAL PARK. By Richaed M. 
Hunt. With a description of the designs. 



Pickert and Metcalf 's Art of Graining. 

1 vol. 4to. Cloth. $10.00. 

THE ART OF GRAINING. How Acquired and How Produced, 
with description of colors and their application. By Charles 
Pickert and Abraham Metcalf. Beautifully illustrated with 42 
tinted plates of the various woods used in interior finishing. 
Tinted paper. 

The authors present here the result of long experience in the practice of 
this decorative art, and feel confident that they hereby offer to their brother 
artisans a reliable guide to improvement in the practice of graining. 



Portrait Gallery of the War. 

60 fine Portraits on Steel. Royal 8vo. Cloth. $6.00. 

PORTRAIT GALLERY OF THE WAR, CIVIL, MILITARY 
AND NAVAL. A Biographical Record. Edited by Feank 
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One Law in Nature. 

12mo. Cloth. $1.50. 

ONE LAW IN NATURE. By Capt. H. M. Lazelle, U. S. A. 
A New Corpuscular Theory, comprehending Unity of Force, 
Identity of Matter, and its Multiple Atom Constitution, applied 
to the Physical Affections or Modes of Energy. 



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Ernst's Manual of Military En- 
gineering. 

193 Wood Cuts and 3 Lithographed Plates. 12mo. Cloth. $5.00. 

A MANUAL OF PRACTICAL MILITARY ENGINEER- 
ING. Prepared for the use of the Cadets of the U. S. Military 
Academy, and for Engineer Troops. By Capt. 0. H. Ernst, 
Corps of Engineers, Instructor in Practical Military Engi- 
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Clmrcli's Metallurgical Journey, 

24 Illustrations. 8vo. Cloth. $2.00. 

NOTES OF A METALLURGICAL JOURNEY IN 
EUROPE. By Johh A. Chukch, Engineer of Mines. 



Blake's Precious Metals. 

8vo. Cloth. $2.00. 
REPORT UPON THE PRECIOUS METALS: Being Statisti- 
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Clevenger's Surveying. 

Illustrated Pocket Form. Morocco Gilt. $2.50. 

A TREATISE ON THE METHOD OF GOVERNMENT 
SURVEYING, as prescribed by the United States Congress. 
and Commissioner of the General Land Office. With com- 
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for the use of the United States Surveyors in the Field, and 
Students who contemplate engaging in the business of Public 
Land Surveying. By S. R. Clevestger, U. S. Deputy Sur- 
veyor. 
" The reputation of the author as a surveyor guarantees an exhaustive 

treatise on this subject." — Dakota Register. 
" Surveyors have long needed a text-book of this description.— The Press. 



D. VAJSf NO STRAND. 43 



SILVER MINING- REGIONS OF COLORADO, with some 
account of the different Processes now being introduced for 
working the Gold Ores of that Territory. By J. P. Whitney. 
12mo. Paper. 25 cents. 



COLORADO: SCHEDULE OF ORES contributed by sundry 
persons to the Paris Universal Exposition of 1867, with some 
information about the Region and its Resources. By J. P. 
Whitney, Commissioner from the Territory. 8vo. Paper, with 
Maps. 25 cents. 



THE SILVER DISTRICTS OF NEVADA. With Map. 8vo. 
Paper- 35 cents. ' 

ARIZONA : ITS RESOURCES AND PROSPECTS. By Hon. 
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Paper. 25 cents. 



MONTANA AS IT IS. Being a general description of its Re- 
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with a Map of the Territory, showing the different Roads and 
the location of the different Mining Districts. To which is 
appended a complete Dictionary of The Snake Language, and 
also of the famous Chinnook Jargon, with numerous critical and 
explanatory Notes. By Granville Stuart. 8vo. Paper. $2.00. 



RAILWAY GAUGES. A Review of the Theory of Narrow 
Gauges as applied to Main Trunk Lines of Railway. By Silas 
Seymour, Genl. Consulting Engineer. 8vo. Paper. 50 cents. 



REPORT made to the President and Executive Board of the 
Texas Pacific Railroad. By Gen. G. P. Buell, Chief Engineer. 
8vo. Paper. 75 cents. 



U SCIENCE SEBIES PUBLISHED BY 



Van Nostrand's Science Series, 

It is the intention of the Publisher of this Series to issue them at inter- 
vals of about a month. They will be put up in a uniform, neat and attrac- 
tive form, 18mo, fancy boards. The subjects will be of an eminently 
scientific character, and embrace as wide a range of topics as possible, all 
of the highest character. 

Price, 50 Cents Each. 
1. 

CHIMNEYS FOR FURNACES, EIRE-PLACES, AND 
STEAM BOILERS. By R. Armstrong, C. E. 

3. 

STEAM BOILER EXPLOSIONS. By Zerah Colburst. 

3- 

PRACTICAL DESIGNING OF RETAINING WALLS 
By Arthur Jacob, A. B. With Illustrations. 

4. 

PROPORTIONS OF PINS USED IN BRIDGES. By 
Charles E. Bender, C. E. With Illustrations. 

5. 

VENTILATION OF BUILDINGS. By W. F. Butler. With 

Illustrations. 

e. 
ON THE DESIGNING AND CONSTRUCTION OF STOR- 
AGE RESERVOIRS. By Arthur Jacob. With Illustra- 
tions. 

7- 

SURCHARGED AND DIFFERENT FORMS OF RETAIN- 
ING WALLS. By James S. Tate, C. E. 

8- 

A TREATISE ON THE COMPOUND ENGINE. By John 
Turnbull. With Illustrations. 

9- 

FUEL. By C. William Siemens, to which is appended the value 
of ARTIFICIAL FUELS AS COMPARED WITH COAL. 
By John Wokmald, C. E. 
10.— COMPOUND ENGINES. Translated from the French of 

A. Mallet. With Illustrations. 
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